Does the new front office hire an established name at head coach? Offensive or defensive-minded? A young fiery hot-shot? I agree that it's imperative for coaching style to match well with Rivers, etc. Here's how I weigh it:
Assuming they keep Pagano, they should hire a defensive HC who can help Pagano solidify what looks to be a promising identity on D. Hopefully that can be a strength while the team rebuilds the offense.
Defensive coordinators for the NFL's top defenses:
Dick Lebeau, Pitt: Will retire as a Steeler and a legend.
Rod Marinelli, Chicago: Strong DC, coached the Lions, we all know how that goes.
Jack Del Rio, Denver: Same as Marinelli but with JAX.
Wade Phillips, Houston: Known entity at DC. Dallas flop too recent a memory.
Gus Bradley, Seattle: Never HC before, but has done well at SEA and is young with upside.
Vic Fangio, SF: I believe has no HC experience but a strong background at Baltimore and Stanford.
Fangio and Bradley are the clearest options. Not so much due to to being more qualified as a defensive coach, so much as they DON'T have a track record of failure as a head coach (and this warrants getting a chance, I suppose)
What about the offense? Bc of the lack of big name, head coach options that bring offensive prowess (Arians) or the right fit (Kelly), I think Spanos and his new GM need to dig deep and give a chance to a young hot-shot position coach as their next OC, and hopefully make the right personnel moves.