it would be more useful to a beginner if y'all would mention WHY you selected these particular pieces. Obviously it's too late to retrofit the previous comments, and doing so for 25 recordings would result in double-wide posts. However, perhaps future posters could explain what motivated one or two of their choices?
Thanks.
Well, I'll go ahead and retrofit mine...
I selected my "essentials" list basically on the basis of trying to cover a representative spectrum of the classical output, not necessarily, though mostly, canonical works, and most, if not all, major genres, within the limitations imposed by the original poster, with a list of recordings that are readily available and which capture performances that are musically unimpeachable. I have mostly stuck to recordings in modern sound, but have also tried to include a few really important performers and tried to cover different performance styles. Of course, the list reflects my personal biases and preferences. I will replace three recordings from my earlier list on the basis of unavailability and for better balance. At any rate, here is the list with brief explanations (I suppose I could turn this into a list on amazon's listmania):
Un viaggio musicale - Il Giardino Armonico - it is always hard to include renaissance and early baroque music in lists of classical recordings, because the forms and aesthetic of that period is rather outside of what followed and there are a plethora of works, few of them easily categorized as influential on subsequent musical development. But I think this very fine disc provides a very enjoyable survey of the Italian Renaissance, which was so instrumental in moving music from the sacred into secular settings and giving us the birth of opera. Il Giardino Armonico is one of the very finest period instrument ensembles, and they play these works with love, verve and a lot of involvement. It is a disc I return to very often.
Monteverdi - Vespro della beata Vergine - Christie/LAF - This is a seminal work of early baroque writing, exhibiting the peak of the development of sacred music from the Renaissance. Monteverdi of course is most known as the composer of the oldest surviving operas, but in keeping with the OP's limitations on box sets, I decided to include his sacred masterpiece here. William Christie should be considered a living UNESCO world heritage site for his immeasurable contributions in unearthing forgotten baroque and renaissance masterpieces. That he is also a masterful performer and one of the most universally beloved voice teachers makes it almost too good of a package.
Bach Brandenburg Concertos - Il Giardino Armonico - The Brandenburgs, as you Palmetto already have learned, are considered pinnacles of Baroque music. Personal bias here, but I am very partial to the buoyant playing of Il Giardino Armonico, who perform these works in the Italian style that inspired Bach, and who play with such rhythmic drive and passion that you want to leap out of your chair and dance. This recording has a place of honor on my iPod and has gotten me through many a dreary workday.
Bach Sonatas and Partitas for solo violin - Hahn - Trying to cover some music for solo instruments along the way, one could have likewise chosen Bach's Well Tempered Clavier or the Cello Suites, any of these are in a sense a microcosm of compositional possibilities. they would influence composers for centuries to come and into the present. Hilary Hahn recorded these austere pieces for solo violin at the ripe old age of 16, one of the most momentous debuts of any musical artist in the last few decades. Her impeccably clean double stops clarify Bach's polyphony like nobody else can. This is simply one of the greatest solo violin recordings ever made.
Mozart Zauberflöte - Abbado - Mozart is another one of those composers who cannot be avoided.

The Magic Flute is his last opera and an attempt at breaking the boundaries of operatic convention of the time. Despite the disjointed storyline, the opera is musically uniquely tightly structured and forward looking, some aspects pointing all the way to late Wagner. Abbado's recording is important in that it shows the present state of music making with traditional orchestras on modern instruments adopting influences of historically informed period performance. Abbado here uses modern instruments, but a smaller ensemble to create lighter textures, greater transparency and allowing the voices to shine. The cast is first rate and DG captured the electricity of a live performance that must have been a treat to see in person.
Mozart piano concertos - Barenboim/BPO - Trying to cover the concerto genre, Mozart is in a sense the classical model from which all others follow, emphasizing the conversational or struggling aspect of the concerto. To me, his late piano concertos in particular are simply some of the finest music ever composed. Mozart was first and foremost an opera composer, and Barenboim to my ear like no one else manages to make the piano sing. That he leads these performances from the keyboard with the stellar Berlin Philharmonic (in reduced numbers) makes these performances singularly interpretively coherent, I find. The box set is a bargain these days.
Mozart Le Nozze di Figaro - Solti/te Kanawa/von Stade et al. - A seminal opera and a seminal recording. Figaro is in a sense the pinnacle of the Mozart/Da Ponte collaboration and contains so much musically and dramatically that would be a model and inspiration for dramatic and comical operas for centuries to come. Solti's recording is one of the first digital studio recordings made and features a cast that is absolutely top flight. Solti was perhaps one of the very few conductors who really knew how to infuse the start-stop process of studio recording with a dramatic arc that make the final product sound musically seamless. Simply a top recommendation for this work.
Beethoven Sym. No.3 Eroica - Antonini - The Eroica is in a sense the work that straddles the symphonic cusp between classicism and romanticism. I am very much in love with this impactful performance by Giovanni Antonini leading the chamber orchestra of Basel, which again shows informed period performance on modern instruments, this time in symphonic repertoire. The revolutionary character of this work cannot fail to be noticed in a performance as driven and well characterized as this one. Comes coupled with an equally fine performance of the 4th.
Beethoven Sym. No.9 - Solti/CSO/Norman et al. - Here, by contrast, we have Beethoven's final symphony performed in a more traditionally romantic "big orchestra" syle, though with Solti you can always be sure that there is no lack of drive and clarity. A timeless performance, really. Solti not only boast some of the best singers and a virtuoso orchestra, he also manages to make sense of some of the more seemingly serendipitous episodes of the finale and gets his singers to sing the a capella parts perfectly in tune. A rarity.
Beethoven Pathetique Sonata etc. - Moravec - Beethoven's piano sonatas mark the point in the technical development of the instrument where the limitations of the harpsichord give way to the more expressive pianoforte, opening new possibilities for composer and performer alike. Recommendations for recordings of Beethoven sonatas are a dime a dozen. There are numerous I like, but I find that Ivan Moravec's selection is especially rewarding for the listener. Committed playing from a performer who has really thought about this.
Beethoven Hammerklavier Sonata etc. - Gilels - The big sound of Beethoven's immense Hammerklavier sonata requires the big sound of the Russian piano school.

Emil Gilels is a force of nature. Capable of myriad nuances of color and dynamics, he could go from the finest pianissimo to the most devastating fortissimos. Exactly what you want in this essential work.
Chopin Nocturnes - Moravec - Moravec again, yes. But what a performance! All the ambiguity, melancholy and really original innovative writing of Chopin captured by one of the most sensitive interpreters of his music bar none. This recording, taped at Columbia University in the 60's, was once a hard to find, secret recommendation for decades among connoisseurs. It is now more widely available on CD and remains the reference recording.
Wagner Lohengrin - Bychkov/WDR - There is a sad, but vocal minority of hopeless nostalgists in the internet who claim that the 1950's were the "Golden Age" of Wagnerian singing. I would really like everyone to hear Johan Botha's effortless, rock solid, sensitive portrayal of the title character in this new recording (alongside a lead soprano who not only hits every note but makes every word intelligible) and see if they can sustain that statement. Wagnerian singing is alive and well, thank you. This all-around superb performance captured in wonderful, spacious modern sound is top choice for Wagner's first mature opera, and the one which I think is most accessible to newcomers to Wagner, thanks to its straightforward story and density of almost constant stage action.
Berlioz Symphonie fantastique - Jansons/RCO - This work is so unique in the repertoire and so unique in terms of orchestration, no collection is any good without a decent recording of it. It is also interesting to hear in the context of Beethoven's Eroica (see above), which inspired it, if for no other reason than to see how far music managed to develop in such short time in the heady early romantic period. A number of years ago, I became obsessed with the Symphonie fantastique and bought or listened to nearly every available recording of it. I still have over 40 recordings of it. I remain convinced that the true innovation and radicalism of this score is not to be found with conductors who superimpose another form of romantic insanity onto Berlioz's explicitly detailed score (a la Munch), but with those performers who follow the score instructions to the letter while retaining a spontaneity in their performance. Mariss Jansons and the incomparable Concertgebouw Orchestra deliver just that. It is the recording to which I regularly return. The disc is also a real bargain.
Brahms Symphonies - Barenboim/CSO - A very personal choice here. There are a number of superb Brahms cycles - Karajan, Wand, Rattle - that I could have likewise recommended (I still await shipment of the Dohnyani cycle, which I hear is excellent). I absolutely adore, and keep returning to, Barenboim's Chicago cycle, though, for its incomparable wealth of color, an intensely dark 1st, a 2nd with a boundlessly joyous finale, and a 4th that simply has the most gorgeous 2nd movement on disc, with instrumental blends, dynamic nuances and a long line that simply has to be heard to be believed. Whichever set one gets, Brahms is essential and will provide a treasure trove of continued discovery. This is the pinnacle of symphonic writing in the traditional classical format and simply has to be in every collection.
Schubert 9 "the Great" - Furtwängler/BPO - Here is an attempt to include perhaps the most influential conductor of the past century. Nobody else is cited as an influence by so many conductors as Furtwängler. His recording of the 9th is not only in unusually good sound, it also shows him, I think, at his very best. The Schubert 9th in the hands of lesser conductors often devolves into a randomly endless agglomeration of episodes and repeats. Furtwängler manages to make sense of this giant work like nobody else can. He shows that the Schubert of the 9th is the same Schubert of the tuneful Lieder, the same Schubert of the endlessly inventive string quartets, and a precocious late-romanticist/modernist pointing the way ahead to the symphonic über-structures of Bruckner. This intellectual synthesis within a performance of immense spontaneity, inexorably organic development and edge-of-the-seat sweep is really what defines great conducting and why Furtwängler remains an unavoidable influence long after his death.
Dvorak Piano Quintets - Richter/Borodin SQ - I almost forgot to cover the essential genre of chamber music. Where would we be without chamber music, which allowed music to be experienced in more intimate settings when large bands were unavailable? We should also cover some of the national romantics influenced by Beethoven and Brahms, who infused classical/romantic structures with the folk heritage of their home countries. Dvorak is the textbook case. His piano quintets have been personal favorites of mine for a long time, since I heard my parents rehearsing and playing them at home. I have found it impossible to find a better played recording than these timeless live performances by Sviatoslav Richter and the Borodin Quartet.
Bruckner 8 - Kubelik/BRSO - Bruckner to me is an essential composer, because of his telescopic synthesis of the distant past and the inklings of a distant future beyond traditional harmony, but within romantically expanded classical symphonic structures, using counterpoint deeply indebted to Bach. The 8th is his last and most accomplished completed symphony. This newly unearthed live performance gives us grand but dramatically intense, yet straightforward Bruckner, by a woefully underappreciated master-conductor who knew like few others how to merge profound intellectual understanding of the music he conducted with natural, unpretentious musicality in performance.
Mahler 5 - Chailly/RCO - Mahler, again for me, is essential for his attempts at containing the entire universe of human emotion and experience within symphonic structure. Of his symphonies, I find that none so comprehensively contains this totality as well as his virtuoso roller coaster of the 5th. No other orchestra in the world probably has as uninterrupted a Mahler tradition as the Concertgebouw, and few others match them in virtuosity. Chailly leads one of the finest performances on disc, captured in the most resplendently spacious sound you could ever want.
Mahler 9 - Barenboim/Staatskapelle Berlin - More Mahler. Like Beethoven, Mahler was one of few composers who developed radically over the course of his productive life while still staying true to some personal, unmistakeable characteristics, which makes it essential to have a little of his output from different periods in his life. The 9th is such an angst-ridden farewell, with its foreshadowings of musical modernity, it is hard not to include it in a discography of essentials. I had to include a link between romanticism and modernity, and this practically defines it. Barenboim's performance is to me the essential recording of this work, for a number of reasons: firstly, it is played with immense sensitivty and great contrast in the various moods of the work, while providing a clear guiding, overarching dramatic line; secondly this is an important disc in that it captures in superb sound a Central European orchestral culture that survives only in very few places these days, mostly in East Germany and the Czech Republic. If we have a list of essentials that includes modern American orchestras, the Berlin Philharmonic and the Concertgebouw, alongside HIP and HIP-influenced ensembles, the dark-hued, rich sound of an orchestra like the Staatskapelle Berlin shouldn't be missing. A nearly equally good alternative that also captures the Central European orchestral tradition would be Ancerl with the Czech Philharmonic.
Strauss Eine Alpensinfonie, Four Last Songs - Harteros/Dresden/Luisi - Then again, here I go including another East German orchestra unique in sound and rich in tradition. This recording is important to me in a number of ways: Strauss's Alpensinfonie to me represents the height of the form of the symphonic poem, which Strauss didn't invent, but arguably perfected. It tells with almost photographic realism of an ascent to and descent from a mountain in the Swiss Alps, vividly describing in music all the sights along the way. This is again a piece I love dearly, and no other recording comes anywhere close in sweep, quality of playing and recorded sound as Luisi's riveting performance with the Dresdners. Thankfully, it is coupled with a very fine performance of Strauss's Four Last Songs, which themselves in a sense represent the culmination of the German art song, albeit with orchestral accompaniment. Written after the horrors of WWII, these works are in a sense almost a farewell to a musical tradition that had already been nefariously appropriated by the Nazis and abandoned by the modernists. So, two birds with one stone in this recording.
Stravinsky Firebird - Boulez/CSO - Stravinsky's Rite is arguably the more important and revolutionary work, but a) I still haven't found a clear favorite recording of it, and b) I find Stravinsky interesting because despite his modernity, and despite his vehement attestations to the contrary, he is a deeply Russian composer, and his incorporation of Russian folklore is more evident in his Firebird, which remains my favorite Stravinsky work. I have heard Boulez with the Chicago Symphony Orchestra live numerous times, and these performances are deeply ingrained in my memory. So this is again a very personal recommendation, but I find that the combination of Boulez's analytical clarity and the CSO peerless virtuosity and inexhaustible musical reserves yield the most interesting discoveries in the early/mid 20th century repertoire. I could have likewise put Bartok's Miraculous Mandarin with the same forces in this spot in the list - another well-worn recording in my collection.
Debussy Piano Works - Michelangeli - Debussy's Preludes in particular and his other solo piano output are to me essential, both in defining impressionism, paving the way towards modernism and breaking the boundaries of musical expression on the piano. Debussy asked for a non-percussive tone on the piano, a technical near-impossibility. Nobody, but really nobody, ever possessed that sort of total control over sonorities and achieved that non-percussive tone like Arturo Benedetti Michelangeli. These are absolutely essential performances for both the repertoire and the mastery of the performer.
Debussy L'apres midi, La Mèr etc. - Rattle/BPO - I know I'm a bit heavy on the symphonists here, but hey, it's a personal list.

Nothing defines Impressionism more than Debussy's Prélude a l'après-midi d'un Faun, and his La Mèr showed that there was still life to be found in grand symphonic structures. This recording with Simon Rattle and the Berliners was a recent acquisition for me, but has quickly occupied a special place in my collection. Top flight woodwinds are of the essence for French impressionist music, and there simply isn't a better woodwind section out there at the moment than the Berlin Philharmonic. This recording is simply a marvel of not just technical excellence but sheer joy of playing and idiomatic expression. A cascade of colors captured in top quality sound.
Ligeti Musica ricercata, Etudes, etc. - P-L Aimard - Of the modernists, some of the works by Ligeti included here are arguably some of the very few modernist masterpieces to really have reached wider audiences thanks to their use by Stanley Kubrick in his films. Pierre-Laurent Aimard is singular among interpreters of the 20th and 21st century repertoire in his sheer technical capabilities, irrepressible curiosity, direct connection to a number of the composers he plays, and his tireless advocacy and inventive programming. This is simply the go-to recording for these works.