I have two suggestions:
- Kansas City Chiefs. They have plenty of starting cap room, and have some surprising talent. They have considerable needs on defense (DE's and DB's as I recall), but are otherwise pretty solid up the middle. Use them if you want a challenge rebuilding an offense, especially in the AFC West.
- Cleveland Browns. Again, they have talent, but the team is a mess. Free agency departures will likely be a problem, but rebuilding this team is fun because they have such poor expectations, that if you stick to one or two focused areas of improvement (OL, LB) then you'll be okay.
Just remember that you shouldn't "cut dead weight" in your second year too much. Your GM skills aren't where they need to be just yet, so don't worry about taking hits in approval rating. Also, when you start your coaching career using a tough team, focus on gameday enhancement skills like "performance" and your focused physical areas. If you're trying to build a solid passing game, pump up your physical skills in QB, WR, and OL areas and hope for the best. Don't buy "ambition" on the special skills list. It's not the bargain people think it is.