I was just offered more quests for the Brotherhood of Steel. I wanted to explore the map instead and figured staying with the MinuteMen is best. Is that a good line of thought? Plus I like the MinuteMen more.

I'm not real knowledgeable on how the factions work in Fallout 4. In Skyrim I could do most quest lines with some variance within them. But from what I read on the internet I can only do one of four quest lines, and if I want those other quest lines I have to start the game over. Is this true?

You'll end up visiting a lot of new areas with the Brotherhood of Steel as well. Especially if you do a good number of their radiant quests from Knight Rhys, Scribe Haylen, and Captain Kels. If you mean the settlements, then yes, that mostly comes through the Minutemen. However, there's no reason that you can't do both. You can, and should join all four of the factions in the game. You can do all four quest lines up to a certain point, and then you have to decide where your allegiances are at. At this point, the game diverges along one of four possible paths. They make a point of explicitly telling you that "by doing this _____ faction will be hostile toward you", so you don't need to worry about alienating yourself from any factions at this point. That's not until later in the game.