Green Lantern Secret Origins by Geoff Johns. It's midway through his run but just start there since it's the remake of his origin from the 60s and 90s.
Then the Geoff Johns run, which started in the 2004 Green Lantern Rebirth mini series until midway through New 52
After that continue through the New 52 series, then the Rebirth Hal Jordan series
That's for Hal Jordan

Green Lantern Kyle Rayner Vol. 1 onwards for Kyle, it is set before the 2004 Rebirth mini series as he became the GL of the 90s. In New 52 he stars in New Guardians. All the New 52 Green Lantern books run parallel with each other.

Simon Baz first appeared nearing the end of Geoff Johns run in New 52, and then become a co-star during Rebirth in Green Lanterns and Justice League
Jessica Cruz first appeared in the New 52 Justice League, and then become a co-star in the same Rebirth books as Baz, and then onto Justice League Odyssey