To get caught up, you don't really need to read all the N52 Superman stuff after convergence, actually I'd recommend you don't, because the Truth storyline is just terrible...
Rebirth Superman 'how it happened' reading order:
Convergence: Superman #1&2 (how they got to the new world and what happened to the old one..sorta)
Superman: Lois & Clark (2015) #1-8 (what they've been doing in the new world)
Superman: The Final Days of Superman (the Trade Paperback collects the issues from 4 different series that make this up this storyline. It's optional, but fills in some holes about what happened to N52 Superman and how the JL met Rebirth Superman)
Justice League (2011) #52 (how Luthor is reacting to the death of N52 Superman)
Superman: Rebirth (2016) One-Shot
Action Comics (2016) #957-962
After that, you can read anything until the Superman Reborn event where Action Comics and Superman crossover and basically retcon the N52 Superman out of ever having existed, lol.
I am REALLY enjoying the Rebirth Superman stuff. I saw 2 comments on the net once: 1st person- but Superman's a dad now... 2nd person- yeah, but he makes it look like so much fun!
Those 2 comments pretty much describe him in Rebirth. He's a husband madly in love, a father loving and training his superpowered son, a friend and helper to the JL, and it's all done with really beautiful artwork I'm really appreciating!
