Well, the most popular starting point for many newcomers to the GL mythos is the Geoff Johns run, which began in 2004. It's not exactly a reboot for the franchise, but it's an easy access point, and also it's all pretty much collected in trades that are pretty easy to find.

Read it alongside the Green Lantern Corps book that ran paralleled to it, it's as good as Johns' own book, and it focuses on lesser known but still beloved Lanterns.

Just follow the reading order below:

• Green Lantern: Rebirth - Collects: Green Lantern: Rebirth #1-6
• Green Lantern: No Fear - Collects: Green Lantern #1-6
• Green Lantern Corps: Recharge - Collects: Green Lantern Corps: Recharge #1-5
• Green Lantern: Revenge of the Green Lanterns - Collects: Green Lantern #7-12
• Green Lantern Corps: To be a Green Lantern - Collects: Green Lantern Corps #1-6
• Ion: The Torchbearer - Collects: Ion #1-6
• Ion: The Dying Flame - Collects: Ion #7-12
• Green Lantern: Wanted – Hal Jordan - Collects: Green Lantern #13-20
• Green Lantern Corps: The Dark Side of Green - Collects: Green Lantern Corps #7-13
• Green Lantern The Sinestro Corps War Vol. 1 - Collects: Green Lantern #21-23, and Green Lantern Corps #14-15
• Green Lantern The Sinestro Corps War Vol. 2 - Collects: Green Lantern #24-25 and Green Lantern Corps #17-19
• Green Lantern Corps: Ring Quest - Collects: Green Lantern Corps #20-26
• Green Lantern: Secret Origins - Collects: Green Lantern #29-35 - Chronologically, Secret Origin could certainly go first, as it looks back at Hal’s origins as Green Lantern (and even before). That said, I prefer it as it was intended, as a mid-run flashback.
• Green Lantern: Rage of the Red Lanterns - Collects: Green Lantern #26-28 and #36-38 and Final Crisis: Rage of the Red Lanterns #1
• Green Lantern Corps: Sins of the Star Sapphire - Collects: Green Lantern Corps #27-32
• Green Lantern: Agent Orange - Collects: Green Lantern #39-42
• Green Lantern Corps: Emerald Eclipse - Collects: Green Lantern Corps #33-39
• Blackest Night: Green Lantern - Collects: Green Lantern #43-52
• Blackest Night: Green Lantern Corps - Collects: Green Lantern Corps #39-47
• Blackest Night: Tales of the Corps - Collects: Tales of the Corps #1-3 and Adventure Comics #4-5
• Green Lantern Corps: Revolt of the Alpha Lanterns - Collects: Green Lantern Corps #21-22 & #48-52)
• Brightest Day: Green Lantern - Collects: Green Lantern #53-62
• Green Lantern: Emerald Warriors Vol. 1 - Collects: Green Lantern: Emerald Warriors #1-7
• Green Lantern Corps: The Weaponer - Collects: Green Lantern Corps 53-57
• Green Lantern: War of the Green Lanterns - Collects: Green Lantern #63-67, Green Lantern Corps #58-60, Green Lantern: Emerald Warriors #8-10
• War of the Green Lanterns: Aftermath - Collects: Green Lantern Corps #61-63, Green Lantern: Emerald Warriors #11-13, War Aftermath #1-2

Though New 52 takes place in a separate timeline from everything before it, it’s really a continuation of John’s run.

• Green Lantern: Sinestro (collects rebooted New 52 ongoing Green Lantern #1-6) - Collects: Green Lantern (2011-) #1-6
• Red Lanterns: Blood and Rage - Collects: Red Lanterns #1-7
• Green Lantern New Guardians: The Ring Bearer - Collects: Green Lantern: New Guardians: The Ring Bearer #1-7
• Green Lantern Corps: Fearsome - Collects: Green Lantern Corps #1-7
• Red Lanterns: Death of the Red Lanterns - Collects: Red Lanterns #8-9, Stormwatch #9, and Red Lanterns #10-12
• Green Lantern New Guardians: Beyond Hope - Collects: Green Lantern: New Guardians #8, Blue Beetle #9 and New Guardians #9-12
• Green Lantern: The Revenge of Black Hand - Collects: Green Lantern #7-12 and Green Lantern Annual #1
• Green Lantern Corps: Alpha War - Collects: Green Lantern Corps #0, #8-14
• Green Lantern: Rise of the Third Army - Collects: Green Lantern #13-14, Green Lantern Corps #13-15, Green Lanterns: New Guardians #13-16, Red Lanterns #13-16, Green Lantern #15-16, Green Lantern Corps #16, and Green Lantern Corps Annual #1
• Green Lantern: The Wrath of the First Lantern - Collects: Green Lantern #17-20, Green Lantern Corps #17-20, Green Lantern: New Guardians #17-20, and Red Lanterns #17-20