The game does such a poor job of establishing the various factions, you can easily be forgiven for not even realising who the Minutemen are, or what they stand for. In another fantastic fly-through of exposition, no sooner have you met and talked to Preston Garvey, that he's offering you the position of 'General', saying how he can't lead his own men anymore (for no reason) and that they need "Someone like you", despite the version of yourself that he's seeing only being in existence for a few minutes. Each other faction goes like this too - fast-tracking from one place to the next. The Brotherhood get one hell of an awesome introduction, only for you to have to piece together what they really stand for from a mix of Paladin Danse's overblown ideologies and leader Maxson's sporadic racism. The Railroad you can track down earlier in the game if you know where to look, but following the main story means that like The Institute, they'll only appear right near the end. There simply aren't enough dialogue options available to get a handle on what each faction stands for in the Commonwealth, outside of a basic reading that you could get from a campaign poster, and that leads to the focus on choosing your allegiance falling pretty flat...
