I actually had an idea earlier today while reading a thread an another board about how redundant Aquaman is on the JLA and someone said he would probably flourish on another team. The idea borrows from Heroes for Hire, when Namor was funding them. AM starts a land-based team and funds them (he runs a massive freaking kingdom, he should be able to throw around at LEAST as much cash as Bats), but also leads them. I'd give him back the water hand (I heard he lost it), I don't care how many writers/editors that would piss off.
I'd put Animal Man on there, beucase I just think the interaction between the personalities and powers of those two would be interesting. I'd also take Cassandra Cain (the last Batgirl) and Catman for the ubiquitous street-levellers. I'd bring in Damage and Ray, and have them develop their powers a great deal in the title, with Ray reaching Dr. Light levels of versatility and Damage gaining much more fine control of his powers, making accidental and tragic releases of stored energy a thing of the past. I duno much about the mystic characters in DC, but I'd want someone like that on the team. Maybe Zatanna. And I'd want a techno guy. Take some random obscure scientist from one of DC's books, have him stumble across some alien tech that supes up his brainpower, turning him into an Engineer type, only replacing the nanotech with an arsenal stored in a pocket dimension that he accesses by thought. He would, of course, have a suit of armor with a few basic weapons, uber sensor suites and a shield generator. I'd probably want a speedster, but I'd probably have to invent my own, since Wally West is taken (or even completely gone, as of IC).
Basically, I'd try to have this team take on threats that haven't shown up on the JLA's radar. Extradimensional army forming to attack Earth? Go kick their asses in before they hit the planet. Some random evil genius designing some new device that might actually threaten the world? Put him down in the planning stages (while still having to fight through his army of evil droids or soemthing).
But yeah. I think the real struggle would be fiding threats that would be credible world-threateners but still write the situations in such a way that would explain why the JLA doesn't just step in and take over first. Of course, this would eventually happen, leading to the usual "Heroes coming to blows over a misunderstanding" scene.
Basically, it would be a fairly powerful team, but one in which no one is made to look like crap to make someone else look good. The title would be one as free from PIS and CIS as possible.