Rise of the Third Army and Wrath of the First Lantern are both arcs in the regular GL books. Granted they are crossovers between four different New 52 titles. Brightest Day was more of a period the entire DCU went through than a GL event. There was a Brightest Day series that came out every other week for several months, with JL: Generation Lost releasing the alternate weeks. However this Brightest Day series was not focused on Lanterns. Its main focus was on characters such as Deadman, Aquaman, Martian Manhunter, and others who all have a connection you will find out about at the end of Blackest Night.
If you want to read Geoff Johns' whole run, you start with a six- issue mini called Green Lantern: Rebirth. Then read the entire 2005-2011 volume, then the first twenty issues of the New 52 volume starting in 2011. If you want to read the other Lantern-centric series which complemented that start with a five issue mini called Green Lantern Corps: Recharge, then flow into the 2006-2011 series. During Sinestro Corps War, this series and Johns' main GL title cross over. The New 52 relaunched this series with a new #1 as well and Venditti and Jensen take over with #21. The New 52 also launched New Guardians and Red Lanterns, both of which are also part of the Rise of the Third Army and Wrath of the First Lantern crossovers, which ended Johns' run. I'm sure if you want to read in the correct order, you'd just have to compare the cover dates on the different series. And Blackest Night was the only thing that wasn't parrt of the regular series, and all the issues of the regular series have a big Blackest Night banner on top while that is happening. If you read in trades, it's even easier. ComicVine should have a list of what issues are collected in what trades on each series' wiki page. And I believe the Sinestro Corps War is all collected together. You could read a whole arc of one series before reading an arc of another series going on at the same time in most cases. Just read the everything before the Sinestro Corps War before it and everything between it and Blackest Night at that point, then post- Blackest Night stuff up until War of the Green Lanterns, then you've reached the New 52. And really the only other thing I could tell you about is Emerald Warriors.
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