My final year project supervisor (I'm a final year undergrad) is offering me a fully funded Phd (with 15k pa stipend) to research machine learning in the genomic space which is super cool and interesting. He studied his Phd at Cambridge and is very strong in his field but the only downside it that I am at an ex-poly very low-rank university.

I have also been accepted at Manchester to do an Msc in AI which I think should lead to a funded phd thereafter and Manchester is one of the best uni's in the country for research in this area.

So , the question is, what the hell do I do?

I don't want to stay in academia after finishing a Phd so I need to know if a) employers will care if I have a Phd from x low rank uni rather than y high rank uni? b) if at a Phd level (people have said) its most important that you get on with the supervisor, like the topic etc and that uni prestige is meaningless at that level ?