Capture the spirit of old-style Gamma World, especially the first and second editions, and of the sources which inspired it or which seemed to draw inspiration from it: Hiero's Journey, Heinlein's Orphans Of The Sky, Metamorphosis Alpha, Kamandi, Thundarr, Wasteland, Fallout, and anything else with mutants and mayhem.
Create a game which is balanced and playable. This isn't a beer-and-pretzels game (though it can be) or one where you create "wacky" throwaway characters. Nor is it one where random luck determines if you're useful. One of the Unchanged is just as powerful as a winged grizzly bear with laser eyes.
Allow for the playing of winged grizzly bears with laser eyes.
Be balanced with standard 4e rules, so there's minimal work involved in taking creatures, or characters, from this game into D&D.