Idea 1: Scientists: We could have two characters investigating a cure for evident radiation poisoning and transformation, and travel across the barren wastes of the country (will put up a poll with names later for you, Laura and Trip if she comes back to decide upon.)
Idea 2: Bandits: We could be leaders of a rogue bandit gng who steal, pillage and kill everything in their wake.
Idea 3: Revolutionary Goverment: We could people who desire a government to reinstalled into the new society of the post apcolypse, but have extreme authoritarian ideals. (Think Half Life 2's society as their ideal)