Trying to get back into the swing of doing things. I admit Batman took me awhile because honestly...there's just so much of his stuff out there. Plus, there's all the sidekick books. For everyone's sake, I'm putting the sidekicks aside and focusing on just Batman. I'll probably make a list of Bat Family books somewhere down the line, but not for awhile.
So, with Batman, there are loads of ways you can approach the character. For the record, as with Superman, if you've seen most of Batman's movies or the animated series, you've basically got a good handle on Bruce's back story. The only thing that might confuse you is the different sidekicks. You probably can jump right into the modern comics if you wanted and skip the golden and early silver age stuff. But that's up to you as a reader. Again, I emphasize that you do not have to read the entirety of Batman's run to appreciate or understand the character. That's a myth made up by gatekeepers.
Note: all of these graphic novels are in reading order as best as I could put them. There are lots more graphic novels in between, these are just the starting points/and or important events in the character's history that it's a good idea to read.
Batman Golden Age Onibus Vol. 1 by Bill Finger
While you don't have to start from the very beginning. If you do wish to for purity's sake, these bind-ups are the place to start. They collect the early Golden Age issues of Batman in a handy chronological reading order.
Batman: Year One by Frank Miller
If you want to jump right into the more modern Batman, this is probably the best place to start. This goes into a lot of Batman's early days and is a good intro to the more modern Dark Knight that people are used too, now.
Batman: The Killing Joke by Alan Moore
This...is not what I'd call a good jumping on point for Batman. I'd only read it after you've gotten to Batgirl and Robin and have read Year One. I don't like it very much personally (sorry fanboys, but I don't). But this is a big event in Bat Family history though. Like it or not, if you talk about Batman, this book will come up and you probably will be expected to have an opinion on it.
Batman: A Death in the Family by Jim Starlin
Another book that is not necessarily a good jumping on point, nor necessarily the best Batman book. But it is an important event that had lasting effects on Batman.
Batman: Knightfall Arc
Knightfall was a big event. I personally got started on Batman while this event was going on. It's...an okay jumping on point. But probably not the best.
Batman: No Man's Land Arc
Another big event that basically started right after Knightfall. Bruce's life was hectic in 90s lets just say that.
Batman Incorporated Arc
This was an interesting new arc that saw Bruce tell the world he was Batman. Warning though, this whole idea got scrapped with the New52 so consider it a odd little AU.
Batman Vol. 1: The Court of Owls by Scott Snyder
If you want to skip all the old stuff and jump straight into the New 52 era, this is a good place to start. There's also Batman Vol. 4: Zero Year, which goes into New 52!Batman version of Year One, but if you've already read Year One, it might get dull for you.
Batman: The Dark Knight Returns by Frank Miller
You've probably heard of this book, even if you aren't a Batman fan. Where does it stand continuity wise? Hard to say. But like The Killing Joke, if you want to talk Batman with people, you will be expected to have an opinion on this book.
Batman: Whatever Happened to the Caped Crusader? by Neil Gaiman
That's right, Gaiman wrote a Batman story at one point. Like the above mentioned Dark Knight Returns, it's not necessarily a part of the canon timeline. Personally, I prefer this one over TDKR but I have a bias where Neil Gaiman is concerned so there you go.