Basically, I am a big fan of the DCAU Justice League. So it’s really hard for me not to say, “we should just make Justice League Unlimited the main continuity and be done with it. They did it. It’s done. Everyone break for coffee.”

But wow that’s simplistic and boring and probably only 97% truthful, so here’s what I want out of Justice League actually.
I love the initial Justice League of the show. The DC trinity built the solid foundation of the show, pulling viewers (especially those of the non-comic-reading variety) in with star power. We all have a favorite amongst Wonder Woman, Superman, and Batman. They’re familiar to us. We also get some comic-authenticity by including the Flash and Green Lantern, but pulling the audience into modern times by using Wally instead of Barry, and John instead of Hal. Not to mention breaking the snow white monotony of the team with John Stewart. (Only Lantern, Best Lantern, I will fight you.) And adding icing to the cake, they brought in less familiar faces with Martian Manhunter and Hawk Girl. I will love them forever for acknowledging the sausagefest they had going, and actually trying to even the gender ratio, albeit slightly.
So it’s a solid team, well thought out. I’d still change it.
Firstly, Batman gets the boot. He’s not the best team player, something writers acknowledge when he formally leaves the League in JL Unlimited. He works better in Gotham, immersed in his special Bat world, building his special Bat family. And while he may win any and every fight (I will fight you over this too), he’s unnecessary in the super-human Justice League.
And I don’t think Superman needs to be there either. He’s got a good thing going for him in Metropolis, and he’s a busy guy as it is. Aside from being the Big Gun in reserve, he’s not necessary. The Flash is, similarly, too busy having his own story and family in Central City (or Keystone, whatever). The league doesn’t need him.
With two-thirds of the trinity gone, Diana is the perfect face of the League. She’s already an emissary of her people; I like her as representing the superhuman collective as well. And she’s never had the same kind of binding ties to a particular city the way Supes or Bats have. Her diplomatic emissary experience make her more than suitable for a public relations role in the core League, representing super powered beings to the public at large. Diana’s good as a character, but best as a symbol.
Like in Justice League Unlimited, Martian Manhunter is the perfect coordinator. His higher brain functions and telepathy make him the heart of the organization. (I imagine that he’d work with Oracle on the side, informally, when he needed the help of another genius.)
With Martian Manhunter as the heart, and Diana as the face, the limbs of the team would Green Lantern and Hawk Girl. John acts as representative and liaison to the greater Green Lantern Corps. in space, but also as an “all-purpose” useful guy to have around. Hawk Girl, with her Nth metal mace, makes her an asset in the supernatural asskicking field. She’s also one of the only League members thus far without a stick up her ass.
Now, in replacing the members we’ve kicked out. Power Girl is basically Super Man only more fun, and it’s always nice to have a Kryptonian* powerhouse watching your back. Big Barda may seem redundant at this point with all the heavy hitters already on the team, but you are wrong. Not only is Barda a valuable asset pertaining to strategic knowledge of Apokolips (those assholes are always causing trouble), but she has fought a dragon. And, you know, she provides essential ground support considering all the other members of the team can fly. She also brings husband and escape enthusiant Mister Miracle along behind her, who may match Hawk Girl in terms of recklessness, but brings a cunning to the team that they probably need. (What with all the powerhouses they’re packing.)
And thus, we have our seven core members of the Justice League.

But they’re only the core members because my Justice League is so much bigger than that.
Screw the League as an exclusive club, it works better if it functions more as some sort of database, union hybrid. I like that they’d have a main team representing the whole of the League and acting as team leaders, but different missions require different talents. It’s best to have the superhero community at large on-call. It also provides a means to coordinate when an earth-shattering catastrophe hits. This allows heroes to still function independently, but also allows them to be called upon if they’re needed. I like to think that smaller super teams can form more easily from this kind of structured community. Groups like the Birds of Prey can have League support, but essentially act on their own. (That being said, Oracle would never register, never exist on a League server.)
Like in JL Unlimited, the Watchtower is a center for superheroes to congregate in and work out of. They build an organized community that effectively uses members to their greater strengths, like sending The Question out to do detective work rather than Aquaman. It always allows heroes to operate independently, but with League support. A League membership card can easily provide insurance as well as access to training rooms. The tradeoff is that when the League is in need of a particular member’s special talents, members are on-call. In the event of a global catastrophe, heroes can efficiently mobilize to more effectively fight their enemies and save people. Everybody wins!
I realize I’ve just written a lengthy fantasy about turning the Justice League into “The Super Hero Resource Center,” but at its source, I think the League is about cooperation and community. It is, after all, a group of people who could easily be at each other’s throats, but instead chooses to unite over a common desire to help people. I just want the Justice League to reflect those ideals no matter the incarnation.
*We are assuming for simplicity’s sake that she is Kryptonian. Peej’s history is so not worth fighting over.