In a post apo world, I’d keep most characters as human. Then you could get something like Metamorphica and roll up random mutations. Re-roll any that don’t make sense or don’t fit your theme properly.
I wouldn’t worry too much about careful balance: the real joy of ICRPG is letting go of mechanical balance and enjoying the emergent narrative. So work with your players to make the rolled mutations make sense - some might give an extra ability, or increase a stat, and others might introduce a flaw or weakness. That’s where the real fun starts!
If you wanted to do “sentient animals” as PCs, you certainly could. Give an uplifted bear a +2 CON to start, and maybe a -1 INT or CHA or something. But they lack opposable thumbs and therefore can’t use most weapons.
Twiddling stats in this way is super fast, easy, and can make a big difference as the game unfolds.