Try getting into it another way - dig out 'concept works' - music written for ballets, like Tchaikovsky's 'Swan Lake' for instance.. there's a story being told in the music, which can in some ways make more sense, than just trying to dive into one or another composers works, without any clear idea of what you're looking for.
A lot of the composers wrote a serious quantity of music - so you can spend a loooong time, just on Mozart, for instance.. (and again, even he didn't write 'one' kind of music, he wrote different types of music, from operetta's, through to specific sounding things for various instruments..)
A gateway to the composers can be by hunting down the uber serious modern players and composers, and listen to their choices.. For instance, Yo Yo Ma has some great choices in what he plays of the 'classics'.. or Michael Nyman (the guy who did The Piano soundtrack) has had a long time love affair going with reorchestrating Mozart pieces, as well as coming up with new modern music..
'Classical' is a HUGE field of music. You could listen to Classic FM or something 24/7 and never even scrape the surface of whats out there... Another way of narrowing things down, is it maybe work out what instruments you maybe enjoy hearing - whether its full orchestra, or solo instruments - and if you can find out what period appeals to you, that can help narrow the field down..
Some movies to give you a sense of the reality behind individual composers - which might help show you bits of music, as well as the real folks behind it.. (off the top of my head)
Amadeus - to show you Mozart
The Music Lovers - to show you Tchaikovsky
Mahler - for Gustov Mahler
Liztomania - Franz Lizt (stupid movie, but still, you'll get some of the music)
Immortal Beloved - for Beethoven
Topsy Turvey - ( for Gilbert and Sullivan) (Victorian comic-opera's)
Others can probably add to the list of movies about composers.. but a couple on the list are available easily (Amadeus, Immortal Beloved) - which can give you a helpful glimpse behind the otherwise dull and boring-seeming genre of 'classical music'.
Often, its helpful to use movies to get a sense of the real guys who were struggling to get their work publicized and recognized, and many had serious issues and problems - whereas the official view as taught in school, shows nothing of the 'real' guys themselves, being would-be muzo's for their times - which is the reality of 'classical music'. It was various ages and country's own versions of pop stars and composers, struggling to make it, in societies that were pretty backward and conservative. One you get a sense of the real people behind the music, it can be an easier task to dive into whichever sound you like.
