Tchaikovsky is a great introduction to classical music, since it's very accessible. His ballet melodies like Swan Lake and The Nutcracker are so well known, that even if you don't know what it is you're already familiar with it. As far as Chopin, I like his Nocturnes a lot, but I especially like his
Polonaises. Check some of those out. If you're really into piano, Grieg's Piano ...