My child is 7 and he has been in 3 schools already. We naively assumed that each of those options would be the best fit for him. We are not done changing schools! We are living in a house in a coveted PS zone and paying property taxes for other people's kids to get the excellent PS education that this school is reputed for
That is how things worked out for us.
We plan to move again before my son reaches middle school - but, we will commute to the new school for a while before moving to the new neighborhood.
If you are looking at private schools, which mean that residency requirements are not applicable, my advise is to try the school for 6 months (commute to it if you can) and then decide to move or buy. If it is a public school, renting first could be a good option. Since you said that high school is your concern, then, while planning your move, you might want to also consider other factors like availability of options for extracurricular activities, enrichment, possible tutoring centers etc.
Good luck.