I came to an interest in some kinds of classical music only recently and find that what I like is just as unpredictable and specific as with any other genre. I have found much classical music I love but can't say I love classical music any more than I can say I love country music. I like what I like, regardless.
The idea of finding a way to sample it broadly and then follow what piques your interest is a good one, rather than buying what is considered by consensus to be the great stuff. I, for instance, have found I really love a lot of Bach's work but that almost all Mozart drives me from the room.
In addition to internet radio I would recommend a site like emusic.com where there are expert recommendations as well as playlists from regular contributors with the ability to hear samples and search for similar music.