Mutants & Machine Guns is a cool little post-apocalypse RPG that come in at around 8 pages. In it, there are guidelines for playing a few types of characters, namely humans, mutants and mutated animals. While this is cool, I feel M&M (not to be confused with that superhero game) can really wander into crazy post-apocalypse territory without really breaking the system. So below are some brief races I think would work out pretty well.
Mutated Plants - Pick a plant type (Cactus: gets Spike Growth mutation; Tree: Gigantism mutation; Mushroom: Acid Spit mutation; Flowering/Fruit Bearing: Enhanced Healing mutation). Rolls 1d6 + 8 for health and gets 2 mutations
Cyborg - Can install 10 TU of equipment into his body, representing cybernetic parts. Can't mutate, but can take up to 20 RP. Rolls 1d6 + 10 HP.
Android - Doesn't need to eat, drink, sleep or breathe. Can't mutate, but can take up to 20 RP. Gains 2 mutations that represent android model. Rolls 1d6 + 8 HP.