My criteria: I would avoid "end of career" coaches so we wouldn't have to hire a new guy in 5 years. (Knocks out K, Izzo, Roy Williams, Larranaga, Kruger etc) I would want a proven track record as a head coach or #1 assistant. (No Price, Wade, Enfield, etc) I would want a clean record in terms of ethics; no scandals or skeletons in the closet. (No Calipari, Pitino, Alford, Scott Drew, etc)
That still leaves a lot of great coaches (who would be impossible to hire)
Bill Self
Jay Wright
Sean Miller
Tony Bennett
Bob McKillop
Shaka Smart