I chose:
Superman
Batman
Wonder Woman
Flash
Green Lantern
Martian Manhunter
Hawkman
I think the Big Seven should all have longevity while also being powerhouses who all bring something different to the team. So the Big Three obviously make it. Flash and GL make it because there have been more incarnations of those characters than any other. J'onn makes it since he's been with every incarnation of the League. Hawkman makes it over Aquaman because Hawkman is straight up more useful in a fight. Though I've always been an advocate of letting Arthur carry Poseidon's trident around. THAT would make him useful in a fight. But even with that, Hawkman can get himself from place to place quickly, and he's also been around as long as Aquaman. Captain Marvel doesn't make it simply because we don't need three people with Superman's powers, and Clark and J'onn win out over Billy for me.