I haven't read Messner-Loeb's run. I have his Flash omnibus that's releasing later year. I've heard good things.
For Cary Bates, I've only read his later stuff. When things started to get stale. Which happens to all long runs authors on a specific title. Grunewald on Captain America, Wolfman on New Teen Titans, Slott on Spider-Man, Bendis on Avengers etc.
However, I'm open to exploring his run for the top 5 spot. Anyone who vouches for it, I'll trust their judgement.
That's a good list. Add up minis to get to solid picture of the character.
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Big Five Justice League:
1. Justice League of America - Gerry Conway (The Satellite Years)
2. Justice League International - DeMatteis and Giffen
3. JLA - Morrison #1-41 + Waid #43-60 + Kelly #61-90 - These could be 3 separate runs, but I'll add them together here to give more runs spots.
4. JSA - Johns and Goyer - Cheating here a little, but the commitment Johns and Goyer made to revive the JSA in the 21st century shouldn't be ignored. JSA likely saw revival because of how successful it's companion title JLA was doing at the time.
5. Justice League Rebirth #1-43 Hitch and Priest