The first part of the trilogy is Green Lantern: Rebirth. But I started with the second part Green Lantern: Sinestro Corpes War and have been doing fine.
Normally you would have to read Rebirth followed by the Sinestro Corps War. But in order to fully understand the entire story line, you'd have to read both GL and GLC from the very beginning following Rebirth. It's a lot of issues but it does help out with understanding all of the clues that have been dropped over the years leading up to the Blackest Night.
If anyone doesn't mind, I can link you guys to the torrent I found, I didn't have the bank for the entire backstory, and I've been reading almost nonstop for the past two days.
So...I just read Tales of The Lantern Corps and GL#44...according to Scar, the Black Lanterns are collecting hearts full of 'splintered light', which is where the small amounts of power they're getting for their rings is going. But it also looks like they're gathering it for the real power behind the scenes, since she was saying 'Soon it will be his turn to rise'.
God I hate this, My local comic shop orders the comics so that we get everything one week after everyone else. And all non-comic shops jack up the prices.
In the good news sector, I just got another copy for another ring to paint, even though I'm probably just gonna get a third and paint the first two.
Normally you would have to read Rebirth followed by the Sinestro Corps War. But in order to fully understand the entire story line, you'd have to read both GL and GLC from the very beginning following Rebirth. It's a lot of issues but it does help out with understanding all of the clues that have been dropped over the years leading up to the Blackest Night.