First of all one should decide whether one prefers a research university or a small college. There are benefits to both and it mostly depends on your psychology. I personally feel that research universities are better because I think that even the basics of the field are better taught by the people who really understand it, and those are usually the researchers. Others feel that people who consecrate a lot more time and effort into teaching make better teachers.
Universities don't necessarily choose better who to hire, but first of all they care mostly about their ability for research and not for teaching - thus accepting people whose main interest is research. Secondly, and perhaps even more importantly, they give their professors the time to do research which small colleges don't. Doing research is not simply some egotistical activity for your own amusement, it advances the field, and more importantly for their role as a teachers, it considerably advances their own understanding of the field, and thus the understanding they try to transmit to their students. This is not only important for graduate studies, but as I said, even for the introductory courses.
Nonetheless, some people would prefer small colleges.
This is perhaps the first method in limiting your choices, presuming one has choices.
Another important factor is specialization. Few know before college what they would want to be, but if you do know, their might be schools which are the best in that field, and those which better than others.
The most important factor, and the first division is implied by the following factor, and that is the school's character. Each school has a certain character. Yale, Harvard, MIT, Princeton, Berkeley, and so on, all have very distinct characters and to choose a school means choosing a character. A character which I should add will effect you considerably.
Harvard is extremely eloquent but sometimes empty. Yale is more aristocratic, Princeton is an old boys club feeling,. Berkeley is huge and egalitarian - it has the benefit of a lot of professors but you will get much less attention than from the small schools. MIT is MIT, and CalTech is if you want to be hazed - it's a school from which few exit without psychological damage (ok, this is partially a joke).
Even in the UC system each school has its character, Michigan, Wisconsin, Ann-Arbor, all have somewhat different characters, Rice, Duke, etc. Each has a specific character which is useful to investigate after you get accepted to them, but I wouldn't go into the trouble until you know you are accepted.
Again, small colleges will have a completely different character, some are even only for women (like Smith, or Wellesley), which some women prefer.
It's important to choose the right character of school for yourself as
you will exit the school with the imprint of the school's character on
your character.