The Wiki for the game is http://www.rpgdl.com/wiki/index.php?title=The_Superhero_Game
Comics that have the feel I'm shooting for include:
Young Justice (now, sadly, discontinued).
Invincible (this is perhaps a little more serious than we'll be in the beginning, but it's still close)
The Teen Titans animated cartoon, and its comic spin-off, Teen Titans GO!
Teen Titans, first volume (the early, early, early stuff, and most emphatically not the newest incarnation of the series).
None of these should be considered "required reading," though they're all good, in my opinion. Most especially, the game is set in a completely different universe from these.