I'd probably go by process of elimination:
Dallas - First one out. Don't want to deal with that owner, even if he signs people.
Chiefs - Second one out. If the rumors are correct that the GM is telling coaches who to start, no way.
Cincy - Third one out. Cheap owners, and you're never going to fix that.
Philly - Fourth one out. I think the owner is pretty active, and I don't want to follow Andy Reid. Plus, that team seems to have some problem children on the roster.
San Diego - Fifth one out. GM seems to be a little bit of a control freak.
Ny Jets - I'd be fine with this team, but it's a bit of a media circus and has a problematic roster.
Carolina - Fine team to take over, but the market is a little small.
Minnesota - Ownership seems stable, good base roster to build from. Could be first, but will probably be second.
Cleveland - If you can rebuild this team, you will be a god in Cleveland. Granted, it's Cleveland, but it's a team with history and pride that really needs to restore its bite. Kind of like the Chiefs, but my impression is that I wouldn't have the GM telling me which QB to start here.
I don't pay that much attention to the dramas on other teams, so I could be missing some big red flag on a team. Honestly, I have no idea what I'm talking about for the most part.
My ancestors fought cave bears so I could make this post.