Choose a major professor and committee

You want an advisor familiar with your area of research who can direct you when needed and have resources and connections you can draw on. Tenured professors have access to more grant money, equipment, and connections, while nontenured professors are more personally available for assistance and advice.
Choose people who you can work with, and who share a common research interest, as well as people you get along with personally. Personal differences often pop up during these kinds of working relationships, making it important to avoid them in the beginning.
Your proposed academic advisor/research supervisor should ideally be named in your statement of purpose, with the reasons you want to work with that person. Those reasons should show that you know something about that persons background and why he or she would make an effective advisor.