While Classical music is used as a broad umbrella, it acutally refers to a particular era from the mid 1700s to the early quarter of the 1800s. While not all the composers I will mention are from the Classical era, they may strike you interest as well; since I prefer the Baroque era composers. Bela Barotk's Hungarain Pictures and Two Pictures are excellent pieces. Then there are Chopin's Preludes and Etudes with feature some impressive piano work as well as establish his signature sound. Then we have Handel's Taffelmusik (water music), but that is more of a Baroque piece. If you have some patience I'd also recommend Brahms Piano Concerto in Dm, Op. 15. But something easier to digest by him would be his Symphonie No. 1. And then there is the one of the masters, that most people know, J. S. Bach. For starters I would recommend his Violin Concertos 1 & 2, The Well-tempered Clavier as well as his four great Toccata and Fuges (D Minor, F Major, D Minor Dorain, and Fantasy in G Major). Then there are Les Folies D' Espagne by Jean-Baptise Lully and Les Indies Galantes by Jean-Phillipe Rameau (both Baroque composers). Then there are the obivous two, Beethoven and Motzart. While I am not a huge fan of Motzart, Beenthoven is another story all together. For Motzart I recommend Piano Concerto in E Flat and Piano Concerto in G. For Beethoven I can say that his greatest pieces are his string quartets and piano sonatas. Listen to Op. 130 in B flat Major, Op. 131 in C sharp major and Op. 132 in A minor. I figured this is too much already, so if you need to find anything more just let me know. Hopefully this will give you a start on your own so that you may begin to explore on your own. Good luck.