For the NFL, I would build a wildcat-option-wing-T sort of team with two quarterback/running backs on the field and put all my money in the offensive line. Player versatility would be the key. The fullback would be the most important player on my team. Jason Peters would have been my fullback.
Imagine just exactly how suckie it would be to defend the endless amount of gadget plays, traps, options, misdirections, counters, and general smashmouthery of this approach.
On defense, I would go for smart veterans and play them in exotic schemes. I guess that makes me part of the Bill Belichek school. Depth would be the key here. I want to be able to have big linebackers for running downs, small ones for passing downs, etc, etc.
Player development would be the difference in my franchise. I would attempt to select guys with potential and sign them to long contracts. My franchise would be known for making players. I think the Steelers do a good job of this.