I don't think anything you posted is a spoiler.
First Playthrough so I've joined every available faction so far, I'll be meeting the Institute soon.
Anyway.....
Minutemen - generally kill Gunners, Raider, Snyths, Super Mutants and Ferals as you gain control of settlements, protect settlements and repeatedly rescue settlers.
Brotherhood - Kill all of the above while finding tech and cleansing the Commonwealth of mutant scum.
Railroad - Kill all the above while escorting run away Snyths, finding DIA caches, planting sensors and clearing out overrun safehouses.
Institute - Haven't met them yet, but I'm assuming your kill most of the above.
The reason you go to the locations depend on the faction, but it generally boils down to killing the usual suspects.