Alright, let’s do this:
First off, if you’re even remotely interested in Batman, pick up Batman: Hush. Brilliant story that pretty much encapsulates his entire universe. By that same token, do not pick up anything with the name Frank Miller on it, as, aside from The Dark Knight Returns (which is iffy) and Batman: Year One, he cannot write Batman to save his life. Note that TDKR is just my opinion though, since most people think it’s one of the best Batman stories ever told for some reason.
Next, look for pretty much anything by Geoff Johns (particularly his New 52 Justice League book).
My personal final recommendation is to get as much of the New 52 Batman book as you can. It’s brilliant, it’s got some of the best stories ever told, and is just really, really good.