The new manager shouldn't be Rafael Benitez under any circumstance.
Take emotion out of the situation and it makes perfect sense. It's manager who was at least once World class, and who has won trophies throughout his career. He'd arguably be the manager with the best track record we've had in a very long time.
However, the decision needs to be an emotional one to some degree. The club's fanbase needs a unifying manager. That wouldn't be Rafael Benitez. The 1st sign of any poor form and we'd almost all want him gone. It'd be a lose lose situation in the end.
The list above is an interesting one. In my opinion a few of those names are unrealistic. I'd be very surprised if a Wenger, Mourinho or Simeone would give us a 2nd thought.
Benitez as stated above shouldn't be considered. I don't think Moyes should be considered either for similar reasons - he wouldn't be allowed the same grace period as a different manager by sections of the fanbase.
Howe looks an interesting candidate. Potter too. Though Potter has a much, much shorter period as a top flight manager. Arteta is the other option. Hard to judge him though. Never been a manager but highly though of coach for the best team in Europe over the last few seasons. Without his ties to the club I'm not sure we'd be so keen on him. However, he might be the one. That spark that's needed.
Who knows though? We still have Silva in place at the moment. I don't think he's sacked anytime soon. Think this run would need to extend for another 3-5 games. Even then a sacking would probably mean a temporary manager and a permanent appointment in the summer of 2020. Don't see Potter or Howe waking from current positions mid-season. Arteta might be tempted though
I'd say they look the actual opposite of interesting candidates. Very dull candidates in fact.