I am willing to apply for a graduate school in US, but I dont know the criteria upon which I will choose where I study. Should I choose upon the ranking or the supervisor??
Both the selection of the university and the supervisor are important. Find a university where you will be happy because you will be there for a while. Try to get into the best university which you can find. If you are a kindred spirit of the supervisor, then you are in the right place. A good supervisor will mentor you and sponsor your works. Remember, you will be an alumni member of wherever you graduate and relations with the supervisor continue even after you receive the diploma.
Sometimes the best fit between a student and a university is to be aware of what others are saying about the department. What type and amount of research is coming from the department? What do recent graduates of the department have to say about their education? You can search websites and social media platforms for more information. Your supervisor is the most important person you need to research. However, your supervisor may change in the course of your graduate school. Good luck!!!