My top choice would be Schwartz for many reasons: (1) continuity (2) players like playing for him (3) Comes from the Belicheck family tree so he has the connections (4) top coaches failed at their first gig, like Belicheck and Carroll so why not Schwartz?
Alternative choice would be Rex Ryan just because he is animated, players like him and he knows the AFC East well. Plus, the rivalry with the Jets would be amazing, Marrone vs Ryan. Def. a Monday night matchup.
I think Frank Reich is too green for HC but would be a fantastic choice for offensive coordinator/assist head coach.