My recommendation is for you to go to Naxos.com and pay the nominal $19.95 for an annual subscription to listen to their entire catalog on-line. There you can listen to thousands of recordings from the most popular (Beethoven, Bach etc..) to the most obscure. Explore to your hearts content and find out what type of music turns you on. When you find a piece you really like, buy a few recordings to get a taste of the range of interpretations.
Some advice:
1) Don't worry if you don't "get" a certain composer. Move on to what interests you. Some composers won't click for you at all (I've never liked Scriabin for example). Others may take some time. There is more than enough variety out there. When I started listening to classical music in college I could not get into Bach and wondered what all the fuss was about. Now (many years later) I think he is at the pinacle of human creativity with Shakespeare.
2) In the beginning, you probably should start with recordings that sound good. Many will try to steer you right away to recordings in the 1930's - 1950's by famous conductors like Furtwangler, Toscanini, Walter and the like - even if they are often tapes of poor radio broadcasts. Don't worry - get to know the piece first. Soon enough you will develop affinities for certain conductors.
3) Go listen to live concerts if you can. Reproduced sound is no substitute for the real thing.
4) Because of the length and number of things going on in a classical piece, it generally takes the newbie several listens before they get comfortible with the architecture of a piece. Just sit back the first few times and soak up the sounds. Don't try to absorb everything at once.
Good luck - it's a great journey you are embarking on.
