It is a well-known fact (and when I say "well known," I mean well known to the entire world, clearly) that I am a Marvel and not a DC. But there's no reason not to give DC a little love. This one will be a bit harder with my relatively-limited knowledge of DC of compared to Marvel. The Justice League of America is the premiere DC team and should reflect that status. The Marvel equivalent is, of course, the Avengers but they are more of a global team that deals with extraterrestrial threats, while the JLA is more of galactic-level force that deals with global and universal issues. A lot of these ideas demonstrate how DC and Marvel are different.
DC characters, for the longest time, lacked the level of humanity and vulnerability that Marvel characters had. This is definitely what appealed to me more about Marvel. But DC characters have their charms too.
The Team
Batman (Dick Grayson): The Leader
Why Dick? Dick takes all of the best parts of Batman (his detective skills, fighting and genius) and adds a layer of comradeship and humanity that Bruce never has. Dick may not be feared how Bruce is, but he would have the members of the team wanting to help him and listen because they are friends. Dick is the leader of my JLA because he has lead multiple teams, lived his life as a hero and grown into the mantel. The fact that he is not Bruce would also add a level of drama, as he would have to live up the man who came before him.
Green Lantern (John Steward): The Projector
Part of the Green Lantern Corps . . . 'Nuff said.
Powergirl (Kara Zor-L): Powerhouse
Powergirl is Superman's equal, owns a massive corporation bringing in billions, is dating Mr. Terrific for some great subplots, and does not have a boy scout complex that frequently rubs teammates the wrong way. Not only is she the team powerhouse, but she could also be the face of the team based on her corporate experience.
Mr. Terrific (Michael Holt): The Brains
Third smartest person on Earth and billionaire, with super science, medical training, and a master of Kung Fu. He is also dating Powergirl, which would add a nice romance subplot for the book. Michael's genius will be key for the a number of "issues" that would occur in the comic.
Zatanna (Zatanna Zatara): Mystic
Zatanna is a mystic powerhouse. She is the premiere go-to mystic for any issue.
Martian Manhunter (J'onn J'onzz): Backbone
Simply put, J'onn is the backbone of the JLA. He has been on most incarnations of the team, with near-Superman-level-strength, a master shapeshifter with an array of psychic powers. O . . . did I forget to mention he can also phase? Pretty much a one-martian team.
BONUS MEMBER:
Starman (Jack Knight): Fan Favorite
I love Jack and read the Starman comics when they came out, and would love to write the character. It would be interesting to write an older Jack Knight that has a kid back on Earth that is concerned that he is falling into his father's footsteps by disappearing for an extended period of time and no one knowing why. His story would be heartbreaking as he constantly tries to do anything to get home.
The Story (Short Version)
My vision for the recently-formed JLA? They are Zeta-beamed (teleported) without consent to Rann by Adam Strange. He believes that his world is about to have another Rann-Thanagar Holy War but there may still be time to stop it. He put out a call but no one responded and he needs to act quickly. The end of the first issue would involve the Zeta beam being destroyed and the heroes coming to the conclusion that they are stranded.
Over the course of the first story arc (roughly seven issues), they become embroiled in a political battle for leadership of a now-unstable Rann and piece the clues together that it is not the Thanagar, but an ancient evil race of aliens masquerading as them to cause the Rann people to start a war and fight on two fronts. The end of the first arc would detail that section of space being sealed off somehow by the ancient evil aliens.
The comic would run for three years in "real" time, meaning none of those characters could have crossovers or be on Earth until the end of the comic. This would give other DC comics a chance to take advantage of the absence of those heroes; the All-Star JLA would have to deal with the aftermath if and when they return to Earth.
And then the question for the follow up series becomes:
What happens to your life, loved ones and identity after you've vanished for three years?