Since you asked a very pertinent question I am replying this in detail. All that is written below is meant for serious students only.
1. Let me answer first whether you should choose a state or private univs.In your case this is important since you are living in USA. You should go for a public univ if in-state fee is applicable to you.I hope that you understand this. If you are a citizen or a green card holder ( there are other categories and norms as well) then in-state fee can be made applicable to you. Mind you in-state fee is almost 30-40% of the normal fee.
By all what I have said it implies that every American or a green card holder should go for a state univ. But it is not so.Why? The answer is that there are more private universities in top bracket than public ones.This does not mean that there are no public universities in the top range.
So you have to see at your end whether you can afford a private or a public univ will do.
2. Next point you should analyze is the program the Univ is offering . Does it’s research areas interest you? Do you feel a professor will take you as an assistant or in his group? Try finding this.
3.Now match your credentials with the univs requirements of admission. See what they want also see what were credentials of admitted students. Apply to univs where you are reasonably certain of admissions. You may also try a few top ones as well one never knows when luck strikes.
4.Check with the univs about their past statistics of placements.
5.Lastly see that the univ has conducive environment to your growth.
Useful data to select the universities is given in the Admission Source Blog.