It's necessary to take the appropriate courses, and study.
If one has a particular discipline of interest, I would suggest reading the journals and identifying the authors with which universities they are affiliated and where the received the undergrad and graduate degrees. Then consider those universities.
No, you don't need to go to a prestigious school to have a good, rewarding career. Your school's name will help you get your first (and maybe second) job. After that, future employers will be more concerned with what you did in your prior jobs than what you did in school.