i would say the easiest way is to buy the digital comics if you dont mind not having the print or buy the trades. you can do that until you are caught up and then buy print or continue with what you were doing. May I recommend Scot Snyder Batman.
Yes because The Nolan Batman would be very different than the JL one or at least I hope. They may not have to make most of the movie an origin but a good amount so you are familiar with the Batman for JL not the Nolan one.