Credit to [link] for the idea. I thought I'd try my own hand at the matter.
I worked with the characters I know the best and who seem to be know the best.

Most of you will probably wonder why I didn't include Doc. Savage. The answer is simple. BECAUSE IT”S IMPOSSIBLE!

Not knowing who the character was until a few days ago, I did research and discovered that the guy can do anything! Would such a character be useful for the team? Yes. Would he work in a fictional setting? No. he’d overshadow everybody. There’s no place to put him. He has no theme because his theme is everything. Besides He probably wouldn’t need the others anyway. So I left him out and figure at the very least, he can be the one who recruits the others for whatever world saving mission he’s got planned for them.

One of the things I hated about the original League was that less than half of them actually had any powers, they threw in Tom Sawyer who wasn’t even in the comics, and Allen, who’s abilities were the same and Dorian’s and Mina’s, lost them by joining the team. (Now That's useful.)

The way I see it you can’t have a super team when nobody’s super so for this I redesigned some of the characters a little, not in just looks but in abilities, so they would work together. Tracy is the only one who doesn't have any abillities. Call him the Batman of the group. PRESENTING:

Dick Tracy: Illinois
Weapons, gadgets, fighting skills, detective skills, and a tricked out car.

The Shadow: New York
Invisibility, shape shifting (illusion based), and Telepathy.

Lady Luck: England
Medieval luck charms, And innate ability to sense when bad things are about to happen and where.

The Phantom: Australia
Good ring protects the wearer. Skull ring induces fear on the target.

Sheena: Africa
Survival skills, stealth, animal communication, and animorphing.

The Rocketeer: California
Flight (jetpack), and extreme piloting skills.

Now, before anyone goes off on me for changing Sheena’s costume, I had to think. Would she not integrate somewhat if she were to leave the jungle and come to New York? Besides I needed a look that fit in with the others. I think the Safari look works to keep the jungle theme. It also contains her original color scheme. The face paint was an added bonus.

I know the Weapons don't exactly fit perfectly. I usually create them in a 3D imaging program and insert them, but this time I just threw them together in Photoshop. I'll probably touch this up at a later time.