Sometimes I feel alone in this course of action, but I've honestly never even considered any of those factors. Call me ignorant, but I have no more idea than a goat which schools are public, private, or whatever is in between. It seems like the main focus for those factors is on both whether you'll be accepted, and how much it'll cost. Cost has never been a concern for me personally.
So, basically, wherever I can get in, and of those, whichever school I like the best after interviewing.