Each time the Recon Team wakes up the world has been different than what the players expected. From radiated desert wasteland overrun with cannibal mutants, to frozen tundra populated with sentient animals, to an idyllic paradise ruled by merciless machines, to death cultists using the bolthole as their temple. Typically we play a session or two in each alternate reality, sometimes more. Basically an excuse to use every game sitting on the shelf and every sci fi movie and TV series. And unread this part if you're going to be a player, it's a surprise.
For our game the characters were all some sort of recon in the Vietnam War and have additional training/skills to help rebuild America. In general they were either Green Beret (army), Seals (navy), Force Recon (marines) or CIA. A prior service from any branch could end up in the CIA if you have a particular character concept in mind. Here is a breakdown of the various Vietnam recon teams from the RPG aptly named Recon.
RECON TEAMS in Vietnam
LONG RANGE RECONNAISSANCE PATROLS
FORCE RECON COMPANY
STUDIES AND OBSERVATION GROUP
If the encounter chart indicates humans roll another 3d6 to determine what faction or tribe they belong to.
There are standard Morrow Project adventures out there you can use, and many other games in the same genre that you can mine for ideas. The games I run are typically a hodgepodge of terrible ideas put together in a nightmare setting from various movies, books, games, and doomsayer predictions.
If you need some ideas here are 50 reasons the world ended