I would argue a cheap public school can be a huge mistake. At least where I'm from, the higher ranked public schools cost the most, and going to a cheap school means you missed 4 years of wages, you still paid some amount of money, and you have a degree which isn't useful. Even in engineering I've seen plenty of managers who won't give "good" jobs out to "worse" schools, and small state schools have unknown reputations and will be the first to get passed up in a questionable job market.

Getting a bad degree from a cheap/bad public school seems like a bad life decision. There is so much more to gain by not getting tattoos and looking presentable instead of getting a degree from a school people don't respect