Classical music is just as varied as popular music. Theres operas, ballets, orchestral, etc. There will be some you like, some you hate and some in between.
I studied ballet for 16 years so tchaikovsky "The Nutcracker", and "Swan Lake" are up there as favourites of mine.
Rimsky-Korsakov "Flight of the Bumble Bee" - again another Russian
Brahms "Hungarian Dances" - German
Prokofiev "Peter and the Wolf" - although written for children is still a good intro. Again Russian.
Rachmaninov?s "3rd Concerto". This was the piece of music that Ben Mendelsson ? or that other actor who always reminds me of Ben, tackled in the movie Shine. - umm, another Russian.
Umm, Im a bit lopsided in that I prefer the more dramatic and some times military Russian/German music. Im not really into Beethoven or most of the operas. But Im sure someone else can help you there.
You have probably heard Ravels "Bolero" and not realised it. - French.
And that opera they always play in horror movies - the name escapes me at the moment.
As for modern orchestral music, Im a big fan of the soundtrack to Bram Strokers Dracula by Wojciech Kilar - Poland. Again losts of strings and drums and DRAMA, baby