I would say the first thing that has to be done is the firing of Tom Donahoe.
I would let the next GM decide if he wants to hire a new coach.
If TD fires Mularkey and TD somehow manages to keep his job, they would be hard pressed to find a real good replacement willing to come in after watching the hatchet jobs done on, Wade Phillips, Bruce DeHaven, Mike Shepherd, Gregg Williams, Gilbride, Rusty Jones, and now potentially Mularkey and his staff.
No one worth their salt is going to want to come in and work for an organization that has no loyalty and dumps peope so quickly regardless if the dumping is justified.
Most of these guys....even Gildbride has proven they are decent coaches when given quality players to coach.