Confession: I've never actually read comics. I'm real tempted to, but the amount of comics is just huge. My friend, who's a big comic book girl, took me to the Comic Book store in Times Square, and I was just in awe with how many there were. Seems intimidating, like I wouldn't know where to start =P
I was never much of a comic reader in the past either. I only just jumped on with DC Comics' New 52, where they relaunched all of their titles with new #1's. I'd suggest maybe taking a look at that list of relaunched titles and seeing if any of them interest you. That's how I got deep into the various Green Lantern series.
Though since Batman seems to be the gateway for a lot of people, there's this guy named Grant Morrison who did some pretty great stuff when he started writing for the main series. This is a fairly accessible reading order I'd recommend that covers most of his big stories:
Batman and Son
Resurrection of Ra's Al Ghul
The Black Glove
Batman RIP
Final Crisis
Battle for the Cowl
Batman and Robin
It looks like a lot, but you can finish most of those in like, a day each. Well, that last one is an actual series, the others are all story arcs collected into a single volume. Despite that generic name, that last one shouldn't be too hard to find since apparently there was never a proper comic series called "Batman and Robin" until the 2009 version.
Might do that. But derp, does that mean I have to buy them. D;
You can procure them through "other" means. They're very easy to find if you know where to look.
Though it is cool to physically have them. I've got a couple single issues and like 10 collected volumes because buying singles was getting expensive.
Tim Drake's cool; I was never too interested in his character though for some reason. Damian's story was so farfetch'd I couldn't get into it at first but it grows on you haha. Dick's pretty awesome as well, but I still got love for the Red Hood.
I enjoy Dick just fine (ohgodwhy) in anything but his own series. Nightwing as a series is so freaking boring, but I loved his run as Batman. Damian was just...hellspawn incarnate when he first appeared, and he can still be like that, but I think he's coming around. It'd be cool to see him in an animated or live action production at some point, just so it really feels like he's cemented as part of the mythos. But then again, I don't even think the general public knows there have been like...five different Robins.
I haven't really read enough about Jason to have a solid opinion on him, I keep meaning to start reading Red Hood and the Outlaws.
