Only franchise mode I work with is Madden, and here's what I do:
I clear the board and do the fantasy draft. No way am I going to pay for the sins of a real-life team's crappy management by going through a "rebuilding" process.
I concentrate on defense, specifically the secondary, and offensive line. If memory serves, here's how my first four picks went in my Madden '04 game (I'm in season 3 so my memory on this is a bit cloudy): Rondee Barber, Brian Dawkins, Alan Faneca, Luke Petticoat.
I also draft people young, cheap and healthy, although Tommy Maddox was a steal...