My question if anyone can help is. When choosing a PhD to do does it matter which uni to go to do it? My dd also wants to become a lecturer at uni too
Good supervisor at not a reknowed uni or go to prestige uni but supervisor is fairly new to the post.
It's not an either/or.
And it is hugely discipline-dependent. In the Humanities, it will matter which university the PhD is from, but that's not the only thing that matters.
And the quality of the supervision is important, but not the only thing that matters. Most decent research-intensive universities will appoint 3 supervisors anyway, so there is aways another voice & expertise.
In making appointments. I always like to see mobility. I think that this shows a robustness of the work and a desire to put your research out there - I'm actually not that impressed by someone who does BA, MA, and PhD all at the same place (even if it's Oxbridge!). Although there can be good reason to stay - access to relevant archives/research resources, expertise etc.
But some postdoc schemes require mobility - at the very least a change from Bachelor's institution to Postdoc institution.
I think that you need a supervisor who is research-active, who has good networks in the discipline: someone who is publishing and/or winning grants and/or visibly active in the discipline.
However, it's almost impossible to predict. 3-4 years ago, in my subject area, there were still some good jobs about. Now it's really drying up. Austerity is hitting, and universities are pulling back. When undergrad fees go down to £7,500 it will get far worse (take note all you complainers about fees - you're complicit in wrecking a really world-class HE system).
But that could change when universities realise they actually do need staff to do stuff like, ummm, teaching undergrads. And post-Brexit when there's a huge skills deficit. And when we replace the lost fees income because of the fees reduction coming, with international student income. And they'll be paying he actual cost of teaching etc, so will rightly demand adequate staffing for teaching!
So in 5 to 6 years' time there may be a few more jobs about than there are now. It's cyclical, but the cycles are increasingly volatile.