Categories as far as I can see it:
1. Untried in the Prem, but with European experience: Pereira/Lennon
2. Experienced in the Prem/won something: Martinez/Benitez
3. Untried in the Prem/managerial experience with potential: Mackay/Poyet
4. Rookie manager/Evertonian: Ferguson/Stubbs/Round
What do we need:
Personally I think Prem experience is very important. Not a deal breaker that would rule out category 1 names, but this is one of 2 or 3 best, toughest leagues in the world, with the most money in it. Is the Scottish league a good enough league where domestic success is of value? Ditto, the Portugese league?
A track record of winning something is what we need, if we're to 'kick on', or at the very least, maintain current standards.
A manager with potential is what we appointed when we got Moyes, but the club is in a different place now than it was then. Which I feel rules out category 3 names, and definitely category 4 names. Was Moyes 'an Evertonian' when he came? No, it should not be a factor at all in the appointment process.
For me, I keep coming back to Martinez (even with his relegation, which I can understand people's concerns but would once again cite Joe Royle as a glowing example of someone who worked wonders at a small club, still finished low down in his three years in the top flight before relegation, but showed he had an aptitude to work at a higher level), and Pereira, who I think has a good rep, good piece on him in the Echo today, and the hope that what he doesn't have in Prem experience, he makes up for in new ideas that could take us forward.
Pereira would be more of a gamble than Martinez, but potentially offers more upside.