Hi Lucy Your supervisor's reputation in their field is more important than that of the Uni. Also, while external funding is reassuring as it shows that your project proposal has been peer reviewed, that doesn't necessarily mean that an internally funded project is inferior. As a post-doc/lecturer you will be judged on your research output (number of papers, grants held) and this will have much more of an impact on your employability than which uni awarded your higher degree.
Whether you like the group you'll be working with and whether you think you will be happy there for 3-4 years is of paramount importance! Good luck :o)