Is It All Random for the PCs

One of the things I like about Gamma World is that PC generation is random and quick. It is very easy to get a group of first level PCs ready to go. However, total randomness doesn't always produce the most cohesive team. No one wants to pay for a Con game and then play a useless character (OK, someone might but its easier to take a working character and make it useless than other way round).

So that means altering the "random" character generation.

Goals for the PCs

No repetition of mutations - why play the same character as someone else.
Balance of types of powers

Extra randomness will be added with the cards that the characters start with, so I don't feel bad taking it out with PC creation.