I genuinely hope we're also considering Mancini and Enrique.
Both of them are clearly too good for international management. Enrique I'm guessing will need more time, not very dissimilar to ETH, as both these managers require their players to have a basic know how of how they want their teams to play, first touch close control short passing, something that will take time to instill in our players and academy, don't think we'll see any immediate success with either of them, but if they're the real deal, then we should be patient and let them assemble a squad according to their needs.
Mancini on the other hand, is more pragmatic and has the ability to get the best out of the players available to him, we've seen that with Italy, and even though he is capable of getting his team to play attractive and effective football, he might not have a ceiling as high as Enrique or ETH. I'm inclined towards Mancini as he not only has PL experience but has also won it, and I take seriously anyone who has won the PL when SAF was managing us.
Then there is Zidane, who is really hard to judge, 3 back to back CL trophies cannot be sheer luck, but neither can we overlook the strength of that squad and the fact that he was working with generational talents at their peaks
Poch would be my last option, as he's only got PL experience, no trophies to show for and his style of football is decent at best.
My order of preference would be like this, if we're looking at the long run.
Enrique
ETH Mancini
Zidane Poch
If we want immediate results
Mancini
Zidane Poch
ETH Enrique