These days most rumours has something to it so to answer the topic title it probably be Marco Silva.
But I would hope we went for one of these candidates:
Arsene Wenger - Bit of a gamble as Arsenal never managed to get back to where they once were but maybe that is because of money and clubs like Man C, Man U and Chelsea more than because his football was outdated? He still made Jack Wilshere and Aaron Ramsey look like worldbeaters at times and always made the best out of young talents. If we would like entertaining football, flair, skills and players good on the ball he would for me be a perfect choice. His training methods and approach to the game would for certain make us look like a real entertaining football team and I would like that more than the Mourinho-kind-of-approach to the game. I would love to see Everton with the lacking flair and creativity it has had since the days of Trevor Steven and the 80s.
Julian Nagelsman - an exciting choice but also a gamble with regards to his age. Probably not a problem in Germany where you got much more disciplined players than the tattoo-marked brats of Premier League. Would he get the more experienced and older players respect? Anyway - probably one of the best choices we could make but may want to go to a much bigger club and Hoffenheim has already announced that he is gonna stay put.
Maurizio Sarri - Done a fantastic job at Napol, playing fantastic offensive football and manage to challenge Juve until the last days of the season. Plays a 4-3-3 with all top3 playing narrow to make space to wing backs (would suit Baines and Coleman) one holding CM and two attaccking ones. When loosing possession they press high and change formation to 4-4-2 and when on the backfoot defends narrow just allowing space in wide areas. This man is gold but why go from Napoli to Everton?
Simone Inzaghi - Could be possible to lure to Everton. Maybe a bit untested and lack experience but made wonders this season with Lazio and is a rising star. And who wouldnt love to see this kind of celebration?