If you are spending your money, go to a top public school. There is no advantage to an ‘elite’ private school unless your family is wrapped up with similar ‘elite’ families. You will never get into their groups or cliques and will only be frustrated. Even to go on a scholarship, the social class thing will be thrown in your face. The leftists are as bad or worse than the more conservative students on this front.
After graduation, no one really cares where you went to college. I see resumes from people at ALL levels of professional jobs, and there is no consistency. Lots of CEO applicants are from large public universities.
But, if you are OK with the situation, go to the school that you feel OK with and that will not put you in debt.