You definitely want to pick up Snyder's run on Batman, and I mean all of it. Start from issue 1 of the N52 launch for it. You'll also want to check out Johns' short lived but awesome run on Superman, and pick up Action Comics once Pak took over writing duties on it. GH already recommended Batman and Robin, and Aquaman, those are also series you want to read from issue 1.
Personally I'd also recommend Superman/Wonder Woman, I think its been a solid and enjoyable read.
Just a heads up about WW the run with the N52 starts of really solid and then drags. It ends up being a story that lasts 36/7 issues and could definitely have been told in way fewer issues. There's moments of brilliance there, but editorial should have made them finish the arc and move on.
Thanks sound good. I think what I like with DC now, as stupids as it sounds, when I get really psyched after reading some issues I can fire up my PS4, boot up Injustice, and take a couple of rounds myself. Thats beside the fact that the comics itself are a great read of course.
MvC3 is not an option for me due not owning X360/PS3.