I discovered much of the classical repertoire (symphonic, chamber, opera, baroque, ... as well as piano) during my seven years at university. Cambridge had a wonderful public library - you could borrow two vinyl records (or boxed sets) at a time, in addition to a number of books. I changed my two records every few days, and discovered reams of music. You could do the same - except that now you don't need to go to a library, as we have youtube. Just listen, listen, listen - you will gradually learn, and you will discover avenues to explore that take your fancy. But it is important to read about the composers and works while you are listening - this is harder nowadays, as in the old days we had extensive sleeve notes as well as thorough booklets in the boxed sets. But Wikipedia will probably have something interesting to say about whatever you are listening to, and you can try to get books which will enable you to read in greater depth.
Where to start? It doesn't really matter. I started with Mozart, because I loved his music even in my early teens, and I went forwards (and backwards) from there.
Perhaps I can give you a few suggestions about Mozart. In addition to the piano sonatas, you absolutely need to listen to his operas - his style is absolutely founded on the interplay of instruments and voices which is at the heart of his operas. And you absolutely need to listen to the piano concerti. They are all wonderful, but perhaps I can suggest in particular K271, K466, K467, K491, K503. And do listen the sublime sonata for two pianos K448, and the quintet for piano and winds K452, and the piano quartets K478 and K493. The quartets and quintets without piano are wonderful; do listen to the G minor quintet K516, one of the few pieces I cannot listen to with dry eyes.
Then there is Schubert - the sonatas, and the impromptus, and the string quartets, and the string quintet are unbelievably wonderful. Listen to Winterreise - it is most important to read the translation of the words while listening, Bleak but wonderful. This is another piece that it is hard to listen to dry-eyed.
Don't forget Haydn. The Creation and the last six Masses are terrific. I find great pleasure in his final sonatas. Listen to Hob XV!/49, 50 and 52 - these last two written in London when Haydn discovered the more powerful English Broadwood piano.
Then there is Beethoven, and the Romantic composers...
Perhaps you should subscribe to a streaming service like Spotify. This would enable you to listen to new recordings when they are released - like I did at Cambridge. There is a sort of frisson of excitement with a new recording, which gives you a reason to listen to that particular music; and which may start a new avenue for exploration. You could subscribe to something like the monthly BBC Music Magazine which has interesting articles, and reviews of new releases.
So as an approach, I would recommend self-exploration, with judicious guidance from various sources.
Enjoy!
