Heh. Just thinking about this and what I'd want in a character select screen. (Because of course I was, since I was trying to fall asleep.)
Personally, the things I'd like to see:
Level / Level Range
Filter side. Yes, you can see the icons, but knowing I want to play redside, for instance, it would be nice to have just those (or those plus grey) show up.
RP / PVP / Farmer. Because why not let you tag some of your own characters. Heck, custom tags would be nice, but probably ridiculously more work than I'd think.
Supergroup name. Not sure if this is able to be "seen" at the character select screen level, but...
AT.