At the beginning, Ranger Station will be your base, after that - church, and later you will be able to move your base wherever you want to. You can move the command center to another place in the later stages of the game. Influence is used when you send someone for resources, while moving the base to another location, building institutions or preparing meals for the group. Points of influence (Influence) are another important 'resource', you earn them by completing tasks or putting items into Supply Locker.