Completing those will naturally lead you to The Minutemen and The Institute. The best way to learn about these Factions is to follow the Main Quest line. Its members won't strongarm you into joining, though specific quests will notify you of potential bridge-burning crossroads that will make you an enemy of an opposing faction. Once you get to know a given faction, it doesn't take long to understand its purpose. Unfortunately, many of the ideals in each faction are in conflict with other factions, so if you're looking to make The Commonwealth a place where everyone can be happy, you're out of luck. They can instill a sense of comradeship and purpose.
Joining factions in Fallout 4 is like joining clubs or fraternities in college.
