If you're looking to truly appreciate the Green Lantern saga, especially with Hal Jordan and Kyle Rayner, I've got a recommended reading order that should offer you a solid and coherent experience.
1. Start with Green Lantern: Rebirth by Geoff Johns. This is a great reintroduction to Hal Jordan after the events of Emerald Twilight and sets the stage for many modern Green Lantern stories. It brings back Hal and re-establishes the lore of the Green Lantern Corps.
2. Next, get into Johns' run which starts with Green Lantern (2005) #1. This series runs for about 60 issues and includes many significant story arcs, such as The Sinestro Corps War, Blackest Night, and Brightest Day. Each of these arcs expands the universe and introduces key characters and concepts, making them essential to understanding the overall mythos.
3. After finishing the main series, check out Green Lantern: The Sinestro Corps War (the trade paperback collects issues from both Green Lantern and Green Lantern Corps). This storyline explores the battle between the Green Lanterns and Sinestro's Corps, which is pivotal in shaping Hal's character and the larger conflict in the universe.
4. For Kyle Rayner, you’ll want to read Green Lantern: Legacy by Gerry Duggan, where he plays a central role. You might also enjoy Green Lantern: The New Guardians series (2011). This features Kyle as he teams up with various Lanterns and is a good exploration of his character post-Crisis on Infinite Earths.
5. To round things out, check out Green Lantern: Warworld Saga. Although more recent, it ties back into the mythos and delivers some cool character moments for both Hal and Kyle.
This order should give you a solid grasp of the major arcs and development in the Green Lantern universe while keeping the continuity coherent! Enjoy the ride, I think you'll have a blast!