As a guy who has Batman as his favorite DC hero, I'd suggest you watch the "Batman Animated Series" WB used to air until they canceled it. The series had the infamous Kevin Conroy as Bruce/Batman and Mark Hamil as the Joker. They're voices are iconic for the characters, and the series was really good to everyone who wanted to know more about the Batman universe (the DVDs are expensive, so use a rental service or download the show episodes).
-If you're interested in a much more psychological take on the Batman characters, then I'd suggest "Arkham Asylum, A Serious House on a Serious Earth" as a great place to start. This comic has a pretty weak version of Batman trapped in a truly uninhibited Arkham Asylum. *In fact, the basis the new game was made from was this very comic, though its darkness far exceeds the game's*
I suggest you read this one before "Killing Joke" because it has a MUCH better analysis on the Joker. If you want to know what goes on in the Joker's brain, a psychiatrist character tells you point blank. (This is also download-able)
--As for what you want to read already, just remember,
NOT ALL COMICS/CARTOONS FOLLOW THE SAME STORY!
In the end you the reader get to decide what story lines you want to believe. I, for one, have a love/hate relationship with "Batman Beyond", a cartoon series that takes place in Gotham's future. Anyway, hope my fanboyness helped, and remember to take it slow, you've got a bit of catching up to do! lol