Living in LA, it's kinda weird to see how few people even care if the city gets a team. All of the transplants keep their old allegiances, and there's a lot of transplants here: I've befriended enough New Englanders here that we could practically consider ourselves a colony. All of the locals are either a) Chargers fans, b) Raiders fans, or c) USC fans who don't care all that much about the NFL. I've heard rumors of UCLA fans being a thing, too, though you never really see them outside of the areas immediately adjacent to UCLA.
Personally, I thought that the Raiders were the best option if LA was going to get a team. Most of the guys in their mid-30s around here are already Raiders fans dating back to their childhoods, so it'd be a pretty seamless transition. Would also maintain the sensibility of the current divisional alignments. If the Bills or Jags suddenly moved, though? Well, LA generally doesn't root for losers--they even turned on the Lakers this past season--and those teams both suck. At least in the Raiders' case, there's a local history here. But if it's just some other team with no history in LA that also sucks... who knows. Maybe it wouldn't matter, maybe in the grand scheme of things nobody cares because good teams don't stay good for long anyway.
Also, if the Jags or Bills moved, they would clearly have to switch divisions, which would create a domino effect where KC probably moves to the AFCE/AFCS, depending on which team moves to LA.
Lastly, I don't honestly believe that the NFL wants a team in LA. LA is most valuable to them as a bargaining chip to extort more public funding out of whatever city is currently in danger of losing its team. I really wish the city would just tell the NFL to get bent, because it isn't fair to the taxpayers of LA, Buffalo, Jacksonville, Minneapolis, St. Louis, etc.