I have a "few" alts, with plenty of room for more; and I'd be more interested in rolling up a fresh character for a project like this.
I'm assuming that, since you list Avengers/JLA as examples of what you're interested in this SG being, there's no real "theme", other than that it's a modern day group.
To ME, the SG name is very important. I've found that it can either make or break RP immersion. I'd suggest that, if you have one, you register it before publishing it here.
I'm also, obviously, curious as to what time/day you're thinking of meeting.
Feel free to contact me ingame at @Captain Valiant.