Post-high education LWers, do you think the place you studied at had a significant effect on your future prospects?

I went to Melbourne University and did an exchange program to UCSD. So I have comparison. I think the distribution of the quality of teaching is sufficiently narrow that it should not play a major factor..

There are careers like politics where personal connection that are gathered during university years are very important.

Depending on the job and your part of the world, personal connection might be a very important factor in carer success. It is more likely that you will would gain more, better personal connection in better university.