I'd say Midwest Brotherhood, or Followers of the Apocalypse

I’d join the New Canaanites. I’m not a Mormon, but if we’re talking hypotheticals I think the badass traders with m1911s and tribal interpreters would be great fun to join

In a world where they aren't killed?

New Canaan is a people, not a place

Minutemen

Brotherhood of steel

If I was on the west coast, definitely NCR. If I was in the middle of the country then it would be the Responders. East Coast would be either the Minutemen (without Garvey) or the Railroad.

I would join the courier or mr house in new vegas

Ncr

Minutemen.