The reality in modern times is that Presidents are largely spokespeople. You vote for a candidate. That candidate brings in a whole team of people. Like 90% of that team will be the same for any Republican regardless of which Republican candidate you pick and 90% with be the same from one Democrat to another. That team isn't just the cabinet, it is hundreds of people. The team is who really makes the vast majority of the decisions. Most of the time, the President's job is to act as the liaison between that team and the public- they're a spokesperson.
Now, that isn't entirely true. There are times when a President steers the team in a particular way. But, that's actually pretty rare. Most often what the public perceives as a President pushing for something is actually a push that has been percolating up the chain from a lot of different quarters for a long time and regardless of which member of the party was in the oval office, it would emerge at about the same time and in about the same way.
So, experience in political leadership roles does matter, but isn't crucial. The most important thing, by far, is which party they're from. Second to that, you have their platform, which suggests how their team might differ slightly from another member of their party. Third, the people they have around them while they're running give you a pretty good idea of how they might shape their team a bit differently.