Hello members of this site! I hope this question isn't too bothersome, but I need to ask some professionals who know what they're doing. Furthermore, I know that this is supposed to be a more technical exchange but I ask you patience with this post.
Too long, won't read: Does it really matter where I go to get my PhD in terms of Job opportunities as well as equipping me for a career in pure research?
So to start, I'm a unique case: I'm 17, about to be a senior in High School and simultaneously about to be a Junior in college. I'm currently a mathematics major with a minor in physics and I'm on track to get my degree in two years, and I'm positive that I want to pursue a Ph.D. in Math and do pure research for basically the rest of my life. I really love doing math and I enjoy every second of it.
However, I'm still confused about the whole graduate school thing. Obviously I'm not one to stay on the beaten path and I've been looking into overseas graduate programs in Japan that are taught in English. I love Japan almost as much as I love math, but I really want to receive the best education possible for my Ph.D. which I'm not so sure these programs can offer, after all, the universities that host these programs rank in the 150-200 range compared to American universities that rank in the 1-100 range in terms of quality (According to the QS ranking system).
I really, really want to study overseas (which isn't an option for my undergrad. studies because of the program that is paying for my college education). But I also want to make sure that I get the best education and that if I do go overseas with an advanced degree from a Japanese university, there will be job opportunities waiting for me when I get back.
Will certain doors be opened for me if I attend a school that I don't necessarily have my heart set on (i.e Princeton or MIT or CU Boulder), over attending one where I know for a fact that I will enjoy my term there (i.e. Tohoku University with the IGPAS)? Is studying abroad for a math PhD unfeasible and silly to even think about?
--Thank you all for your time!