Not nearly enough information to decide.

If my headcanon for the Brotherhood turns out to be right, then they are by far the coolest faction, and may or may not be in line with my character's beliefs, depending on how the Minutemen turn out.

I'm definitely going for the BoS as soon as possible. High techy techy is too good to resist. As for exclusivity, I'd only accept joining a faction exclusively if there were a good reason for them to be opposed to other factions. I mean, if the BoS and the Minutemen had opposing goals, I would understand having to choose, but if the Minutemen told me, "No, we don't like you because you hang out with those tin can guys that we never even interact with", I'd tell them where they can stick their tri-corners. It'd be like someone telling you that you can't be a fan of more than one sport.

Brotherhood of Steel just to see the look on their faces when I am like "Oh, BTW, I am from the past so I knew things in my everyday life that you don't have now. Ask away kthxbye"