What advice do you have for a parent thinking about elementary schools for their child?

My first son is almost 3, he’s been in a Montessorri program since he was 1 1/2 so clearly I am someone interested in a school with a philosophy…soon enough, I will start looking for an elementary school and obviously I don’t want him to go to just any old school but I am not paying for it either as I think public schools are perfectly fine..what are some of the things you’ve encountered in your decision-making process about this? and what assumptions have been overturned for you…as in you thought it’s important to put them into an arts-focused school but it didn’t work out the way you thought…