I think the mistake that students make, nowadays, is only looking at schools that have “prestige” associated with the name of the schools.
Consideration for paying for those schools is often an afterthought.
Scholarships, at less prestigious schools, which can be better than the “name-brand” schools, aren’t given a second look.
You need money to attend. The schools that have money to give to you aren’t name brand, that’s why they have money for you. Find a good school with decent merit money for your stats.