Just my two cents on what sort of experiences would make a good president:
1. Former governors: they have some idea of how to be a chief executive of a state, which is some ways is not dissimilar, although they tend to be weak in foreign policy areas, although this isn’t hard to figure out (US wins, everyone else loses is usually a good starting point).
2. Former military officers: My preference here is someone who worked his way up to high rank from the bottom, saw combat and actually killed some of the enemies of this country themselves, so they have some knowledge of what war is really like. This sort will be more likely to have clear goals and be able to make decisions quickly, and be able to work as the head of an organization.
3. A right-wing academic (yeah, I know- that’s so rare as to be legendary..) with extensive knowledge of war and politics who has some of the characteristics of 1 and 2- have served in the military at some point, been a politician of some sort, or both. ‘Book learnin’ can be a useful adjunct to someone of limited experience.
To sum up, someone who understands both war and peace,and can wield extensive power competently and wisely.
You’re right that governors do have experience running something which isn’t wholly dissimilar to a country, and they can be weak in foreign policy areas. I don’t think we’ll be electing a military leader again for a long time. The country is very different from what it was in Eisenhower’s or Grant’s or Jackson’s day. And intellectuals also can be trouble. One with diplomatic experience might work out.