For Bats, you could go for essential reading like: Year One -> Long Halloween -> Dark Victory -> Killing Joke -> A Death in the Family, and then you'll be able to jump into completed sagas like Knightfall and No Man's Land. By that time you will reach the Hush setting and you can read more recent stuff.
And not an Marvel/DC comic, but I recommend you "Invincible" on Image Comics . It's a great spin on the superhero genre (once I read that the premise is something around the lines of "What if Spiderman had Superman's powers"? and it's very accurate to an extend), and it's friendly for new readers, too. The first issue is also free on
digital.
And speaking of Super, you can try All-Star Superman, it's a great read and you don't need to know too much about Superman aside from the basic mythos (As an example, a friend who only knew about Superman by the Donner's movies got to read it and he was blown away)
