I think Lewis would be my top choice. He has home run potential - the problem is, if you hit it outta the park, he's gone within a few years. But maybe he gets you back on the map and then you can go from there.
If Mendenhall has interest, you have to interview him and give him serious consideration. 11 straight bowls at BYU, give him a pass on the 2-10 season year one at UVA, then he rattle off three straight bowls, 5-5 in 2020 and declined a bowl, 6-6 in 2021 and bowl cancelled due to COVID issues. So that's one sub-500 regular season in 17 seasons at BYU/UVA, and it was year one turning UVA around. I doubt he has interest, but he's gotta be on a short list if he does.
I'd be shocked if Chris Petersen has interest, but if he does, that's a no brainer. 14 straight bowl games, 92-12 at Boise State, 55-26 at UW.
I don't have much interest in White, but if they go that route the important thing to me is to find a highly competent OC who's not going to have one foot out the door. Ideally they'll prioritize OL and be able to recruit decent QBs. I'd ask Marrone how much he'd need to come be OC here. He's not going to get another shot as an NFL head coach, you can pay him more than he'll get as an NFL OL coach if you're willing, and I think his style of offense would compliment a Tony White team well. Grind it out, rely on the defense, recruit some good OLs and see if you can use the OL as a hook to get a good QB now and then. It could work. Not my preferred choice, but if they go that route it's important IMO to find a good OC who's not a young up and comer who's going to be snatched up right away. I dunno if Marrone would come play second fiddle at a place he was HC once already, but it would be a step up from his current gig.
Candle I'm not sold on. He inherited a winning program, won with his predecessor's players his first two years (9-4, 11-3) then rattled off some ~ .500 seasons, and now has a couple strong seasons. I feel like he'd end up being a replacement level hire.
Anyway, outside of the longshots I doubt have interest, Lewis is the winner in my opinion.