About the rank issue:
I'm quite worried about carrer prospects after the PhD. What are the things that matter for this?
-How well they teach you what you want to learn.
-How well they teach you what to want to learn - in order to be successful on the job market.
-Opportunities to network (that includes research centers, research assistanceships, travel money etc).
-Training\experience in teaching, programming, and other transferable skills.
Isn't everything else secondary with respect to making this thing a career? And do rankings reflect how well programs offer these things?
My guess is that name recognition only matters if you leave the academic discipline.