My list of essentials. I know these are essential (to me), because I did a major cull in 2000, and these are among the ones I kept. Most are the versions I bought when I started collecting in 1987, which I read about in Gramophone or the 1986-1993 Penguin Guides to Classical Music. I also had four friends who knew a lot about classical, including a piano professor at a university and a music critic whose name most of you would recognize. They all loved taking me shopping. However, after a personal tragedy, by which time I'd gotten up to around 2500 CDs, I cut back to around 500. Here are my favorites from the 500.
N.B.: Most of my recommendations are from what was available in the late 1980s and early 1990s. I imagine many will have been superseded by later, better recordings, or at least better sounding recordings. So, I suggest you explore other versions in addition to the ones I am recommending. Some, I'm not recommending anyone's version. The pieces of music themselves are definite, unqualified recommendations, however.
Also, buying box sets seems to be the only way to get a lot of music these days, and it's available at such a better price than what I paid thirty years ago. So buy box sets when you can.
Mahler - The Symphonies - Bernstein, Sony
Mahler - Symphony No. 4 - Karajan
Mahler - Symphony No. 5 - Bernstein, DG
Beethoven - Symphonies - Harnoncourt, HvK's 1977 and 1963 recordings on DG
Beethoven String Quartets - Takacs or Emerson Quartet
Beethoven Piano Sonatas - Paul Lewis or Andras Schiff
Bach - St. Matthew Passion - Herreweghe 1984
Bach - Well Tempered Clavier I Schiff
Bach - Well Tempered Clavier II Schiff
Bach - Goldberg Variations Schiff
Bach Brandenburg Concertos Pinnock, Akademie Fur Alte Musik Berlin
Brahms - Symphonies - Abbado or Honeck
Mozart Piano Concertos Brendel, Perahia, Uchida: modern piano; Bilson, Levin: HIP
Mozart - Symphonies 25-41
Mozart - Le Nozze di Figaro
Mozart - Die Zauberflote
Puccini - La Boheme
Schubert - String Quartets and Quintet
Schubert - Piano Trios
Schubert - Piano Sonatas
Shostakovich - String Quartets
Sibelius - The symphonies - Ashkenazy
Verdi - La Traviata
Vivaldi The Four Seasons Pinnock
Vivaldi Alla Rustica Pinnock
Vivaldi Lute and Mandolin Concerti Paul ODette
Also, do check out the chamber music of Brahms, Beethoven, and Schubert that I have not specified on this list.
ETA: I checked out how much it would cost to buy all of this new on Amazon, and I got 22 items in my cart, costing between $500-600. When I started collecting classical, a single box set of, say, Mozart Piano Concertos cost between $160-200. I remember paying $212 for Inbal's Mahler box set. Good time to be buying classical.