Hi there! Welcome to Chaos. ^_^
Factions are an entirely optional portion of the board. You don't have to join one at all, you can join as many as you want with any characters you want, and you can leave whenever you feel like it. Not all factions accept walk-in members, but most do. If you find one you like that says "you do not have permission to join this faction" on its page, you can usually just PM one of the faction reps to get added.