For me, the only criteria is an ability to implement an effective style of play.
That doesn't mean fancy - Conte's style is quite dull, but it's effective. (Not that I'm saying Conte is an option, either.)
I would rule out anyone that hasn't done it at at least two/three clubs.
Potter, Hasenhuttl, Knutsen (successful rebuilds rather than another club), Bielsa and even Marsch fit the bill, for me.
I'm doubtful of Muscat just because he has only done it following Ange - can he implement that style himself, from scratch? I don't know. He failed in Belgium.