One approach would be to build on what you already have liked: Check out some Mozart symphonies, some of his string quartets, his operas. Do the same with Tchaikovski--there's a lot more to him than the two works you mentioned. You could also start listening to music from the same time periods as these two. Check out Haydn, Borodin, Brahms. Then look at a few composers from earlier periods, Handel, Bach, Telemann; or later, Beethoven (later than Mozart but before Tchaikovsky), Mahler, R. Strauss, Schoenberg.
Once you've got a few different selections under your belt, you might start noticing that you're gravitating towards string quartets, or symphonies, or whatever. You can then start looking at other recordings from the same performers you've been listening to and if you find things you like, then try others by the composers on those recordings.
Lastly, the hit-and-miss approach has a lot going for it. "Classical" music is such a huge genre that you might never make your way through even a small part of it if you are too systematic. It would be hard for Tchaikovsky to lead you to Percy Granger, Arnold Bax, or Rodrigo, but grab the occasional random CD and see what new vistas (if any) open up. Have fun!
Once you've got a few different selections under your belt, you might start noticing that you're gravitating towards string quartets, or symphonies, or whatever. You can then start looking at other recordings from the same performers you've been listening to and if you find things you like, then try others by the composers on those recordings.
Lastly, the hit-and-miss approach has a lot going for it. "Classical" music is such a huge genre that you might never make your way through even a small part of it if you are too systematic. It would be hard for Tchaikovsky to lead you to Percy Granger, Arnold Bax, or Rodrigo, but grab the occasional random CD and see what new vistas (if any) open up. Have fun!