(4/4)
>OK, on with the actual answer now:As mentioned already, the importance of the institution diminishes (but does not dissapear completely) as you get higher up the education pyramyd, also the importance of the individual increases when going up. It matters more what you know and can do than where you learned it.
The research topic is very important - better do research on a good topic in an irrelevant university than research on a shitty topic in a good university.
Because a lot of your work will likely relate to the competence of your research advisor, their competence in your selected field and your good relationship with them is very important and carries more weight than the institution itself.
TLDR: the PHD is what you make of it, your motivation and knowledge/skill have more to do with success than the name of your university.
Idk what you will make of this answer, but here is some silver lining - even though a prestigious name can open a lot of door for you, it won't do the work for you - you will have to do it yourself.
https://www.sciencemag.org/news/2018/06/prestigious-prize-overshadowed-crispr-researcher-wins-spotlight 
