OB are you talking about incidental music or musical score? One of my favorite films 2001 A Space Odyssey by Stanley Kubrick has a great score. They used music by
Strauss. Below is a sample:
YouTube - 2001 A Space Odyssey Opening
A Clockwork Orange, also by Kubrick made use of music by
Beethoven. Below is a sample:
YouTube - A Clockwork Orange Soundtrack - Ludwig Van Beethoven - Ninth Symphony, Second Movement
Musical scores are not exclusively classical though. Another one of my favorite films, The Virgin Suicides used an Original Score by Air which is synth-pop.
There's an ocean of classical music to choose from and hundreds of composers per era (baroque, classical, modern, impressionist etc) You can't so wrong with Bach, Mozart and Beethoven. Personally I just listen when I am in the mood with the collection of my parents but I'm no enthusiast in classical music.
I also noticed that people who listen to classical music have a good ear on instruments and movements so if you do succeed with your "education" on classical music you'd benefit more from just increasing your brain power
For contemporary film scores the big names are: John Williams (Star Wars, Jaws, Schindler's List), John Barry (Out of Africa, Somewhere in Time) and Hans Zimmer (Gladiator, The Lion King)
One thing about living in the Philippines is that there's so little activities that have to do with culture and art. Good luck! he he.