This is one of the games I'd love to run. I think having only one player is incredibly easy to deal with if you are running a supers campaign. You just need to come up with a few memorable supervillains and maybe one Cobra/VIPER-style evil organization, and you can play forever.
There are thousands upon thousands of old comics to steal stories from. If you use well-known villains like Dr. Doom or the Joker, your job becomes even easier.
Any power level will work, because you don't have to worry about balance at all. I'd personally love to play in a lower-powered game, with characters roughly equal to Spiderman or the Punisher. Then again, a run with someone on the Superman level would be awesome, though I'm not sure if I'd want to make a full campaign of that.
Cosmic heroes really seem difficult to do for a long term campaign, unless you really want to create a bunch of dependent NPC's and spend more time playing soap opera instead of thrashing villains. I'm sure some groups could do it well, though.