Assuming Kirk is accepting of all this and stays on, his history would suggest that he will promote from within. I personally don't see him as a step in the right direction, but I wouldn't be shocked to see Budmayr promoted to the role. Hopefully, the powers that be will factor in that he has had at least a limited role in this offensive mess. Obviously, Woods is a favorite for many of us but does his resume warrant it at this point? A better role may be ST coach/Co-HC.
If Kirk stays and looks outside the program, I'd keep an eye on Chryst as mentioned above. Another would be Akron coach Joe Moorhead, the former PSU OC. Kirk could bring in a young up-and-comer but his comfort zone seems to be more geared towards guys that he knows that have been around awhile.
My personal choice would be Geno Guidugle, the QB coach at Notre Dame. He'll end up as a very successful OC somewhere. There's also a lot of buzz around Kansas QB coach Jim Zebrowski.
If Kirk is bitter about any of this and hangs it up at the end of the season, then obviously all bets are off. In that scenario we should be calling Ryan Grubb the next day.