New to classical music

Edvard Grieg has been mentioned in passing, but specifically, try "Peer Gynt".  Lots of drama in there, and you will recognize a few of the melodies from movie soundtracks, tv commercials, etc.  Make sure to get a full orchestral version since there are other versions (e.g., solo piano, etc.) that wont' give the full effect.

Mozart. That's all.

Lots of great suggestions here.  Just dive in.
rpeluso -- I saw Pollini, too.  Started off with Chopin, and finished with one of those wild banging pieces he has a predilection for.  His hair was flying.  Many conservative concertgoers walked out.   I loved the heck out of it!