Honestly, what I would do is read the Wikipedia page on Hal Jordan up to Green Lantern: Rebirth, give that another shot, then read the trades (which are actually a lot more accessable than Rebirth, since they focus on reestablishing Hal Jordan as a character than they do with all the stuff that's come before). Keep in mind they are writing the character for people who grew up with Kyle Rayner, so they've been reestablishing virtually everything.
The Flash is very accessible as well, though if you get the trades, it would probably help to read the introductions when applicable.
Reading JSA is also a good idea, not so much for the original run (which is good), but for when the book picked up again after Infinite Crisis, where it has been phenomenal issue after issue.
I am also in the Pro-52 boat. I love 52, and it holds up especially well in trade form.