I'm amazed that no one has yet mentioned Also sprach Zarathustra, by Richard Strauss. Also, lots of other works by Strauss. For an excellent idea of how much a particular composer can vary in style from one work to another, try listening to Prokofiev's First Piano Concerto and has Symphony # 1 "Classical," which he wrote, as he himself explained, to show what he thought Haydn might be writing if he had lived on into the early 20th century. Of course, the central 20th century work, around which much of the rest revolves, is Stravinsky's Le Sacre du Printemps. Without going into detail, if you liked Hunger Games, you'll like Le Sacre. Most folk agree, btw, that Boulez's recording of it with the Cleveland Orchestra is the best one. What with the World Series this year being between the Cubbies and the Indians, you might want to consider that many of us also believe these two cities happen to have the two best symphony orchestras in the country, and explore some of the work of each in conjunction with watching the WS--especially recordings by Reiner, Giulini, and Solti with Chicago, George Szell with Cleveland, and Pierre Boulez with both. If you are sympathetic, as I am, with the #BlackLivesMatter movement, you might want to listen (its on YouTube for free) to Janet Baker singing the aria "He was despised" from Handel's Messiah with Charles Mackerras and the English Chamber Orchestra, whose 1966 recording of Messiah is, INHO, the greatest ever made.
I urge you to reconsider your disdain for backstories and tales of composers' lives and how they influenced their work. Such a familiarity is essential for understanding the full import of much of the work of Prokofiev and Shostakovich, for example. For Shostakovich, I recommend starting with his piano quintet, a masterpiece written during WWII. Although it was awarded a Stalin Prize, anyone who knows the backstory knows it was heavily influenced by Shostakovich's hatred for much of what Stalinism represented. In fact, the worst recording of it was made with Shostakovich himself at the piano, because it was recorded in 1955, in that brief 16 month or so period of optimism after the late 1954 de-Stalinization speech by Nikita Khrushchev and the brutal spring 1956 Soviet suppression of the Hungarian Revolution.
I think its a really good idea for you to abandon your desire not to know much about the forms of classical music and how works are constructed and developed, because enjoying them at any but the most superficial levels increases your appreciation of them. Having said that, I must also say that if you play a Bach concerto, say, underwater in a large aquarium, you will see the fish gathering around the speakers, beating their tails in time with the music, with species that are ordinarily enemies co-existing side by side. At a very basic level, all you need to like at least some classical music is to be as smart as a fish. But the more you know, the more it helps. OTOH, don't let it obsess you to the point where you get upset if you lost track of the plot of an opera and don't quite understand all the transitions for one scene to another and of who is singing to whom and what their relationships are. Be relaxed enough to enjoy the music at a fundamental level. In other words, try to study the details, but don't let a failure to keep track of things upset you or keep you from enjoying the music at a more basic level.
To this end, I suggest that violin concerti are an excellent entrée to the world on classical music. Because of the limitations of the violin, what is called the development sections of movements are relatively simple, transparent, and easy to follow. Becoming familiar with these simple development sections will stand you in good stead when you decide to expand to more complicated works. Start with the three Bach Concerti (Hilary Hahn), Beethoven (Grumiaux/Galleira), Brahms (Szerying/Monteux), Bartok2 (Perlman/Previn or Chung/Solti--the Perlman is the best, but it is, to the best of my knowledge, available on CD only as part of a massive set you may not want to shell out for). Try Menuhin for Mendelssohn.
Mahler symphonies are very involving. I recommend the Kubelik as a starter set. I have about 20 or more sets, including two by Bernstein, and the Kubelik is my overall favorite. My favorite of the symphonies, personally, is # 2 "Resurrection." Kubelik is a favorite here, along with the Bernstein performance that is not part of either of his complete sets--its a stand alone performance with Janet Baker as one of the soloists. Its very much like his first recording, but with better vocal soloists. The classic Otto Klemperer recording is another favorite, massive and granitic, and with an absolutely orgasmic finale. You might want to try a Wagner "bleeding chunks" album or two. They're called that because they are purely orchestral versions of part is his operas, or, as he called them, music dramas, and where they end is sometimes a bit arbitrary. George Szell and the Cleveland Orchestra did a couple of good albums of these, now on CD. And, if you want great performances of light classical music which is lusciously beautiful and uncomplicated, you can't beat the Reiner/Chicago album of the five most popular Strauss Waltzes.