Lex Luthor is definitely in the Criminal Faction.
I agree with all the other stuff people are saying too, especially Jonah Hex in the lawman faction and Poison Ivy, Bob, and Deadpool in the Insane faction.
Plastic Man definitely goes with the JLA as well.
For teams, I think you should just stick "Classic" before the titles and then keep Spidey and Surfer out of the Avengers and anyone other than the first four and She-Hulk out of the Fan Four, for instance.
Then, as you suggested, you could have a sub category, like "Avengers Variations" where you could put "extended family members." Heck, you could do that for the X-Men ("X-Men variations") and probably list just about all of the Brotherhood!
If you want to keep the top just synergy based, though, you should probably go with a "Mutant" army based around Professor X, and then save the X-Men/Brotherhood team split for later.
Oh, and I'd say Professor X, Jean Grey, and Martian Manhunter make for at least a Telepath Faction Bud, with more help coming eventually!
P.S. I'm adding this to the Public Directory!