A look into classical

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!

Another approach is to use your computer- go to pandora.com and register. It's free, no worries.
Go to genres, classical and you can select what you want. Chamber???
Internet radio, without commercials. I have found this an excellent way to discover great music, then hit the stores.
Good luck.

Well since we don't really know what you would like, and apparently neither do you, IMHO recommendations would have a very limited value at this point in time.

What I suggest is that you check out from your library some 'compilation' CD's which have the most popular music of various composers. From these CD's you can find music that is appealing to you (actually specific pieces) and come back as ask from recommendations of composers/pieces to build on that particular recording/composer or style.

Another alternative is if you have a classical music station just listen, what catches your ear? Then go get a CD that has it and see what it is combined with and go from there. It is a bit of hit and miss but over time you will find what your attracted to and have built up a collection of things you like as well.

Pandora is a great site. You can listen to radio stations on the Internet such as the fine Dallas Classical station WRR. Also, you might want to try a few audiophile classics from Telarc or Columbia Masterworks. Gramophone and BBC Classical magazines do a tremendous job of sorting things out and publish recommendations each month and summaries of the very best each year. Wonderful things are happening around the world in this genre'. Good luck and enjoy!