Relation of concepts "related work"/"background"/"preliminaries"/"state of the art"?
Every scientific work needs to establish its context.  What exactly you name the sections and how you organize them in order to present this context is less important, so long as you give the reader a good roadmap to understanding how your work fits into the larger intellectual environment.

Personally, I find that references tend to cluster into a few distinct groups:


Motivation of the work and the foundations that it builds upon
Contrasting to the works of others that do not accomplish the same goals, showing that you are aware of them and that your work is novel.
Justification of assertions
Pointers to methods that have been used


The first two are what typically ends up in a related work / background / whatever section, while the other two more typically end up embedded in other prose where they end up being relevant.

Given this, your proposed structure seems basically sane, though of course the details can't be determined without knowing the details of your work.  The most important thing, I would say, is that if you end up with a very large and complex chapter (as often happens in a thesis), to make sure that you give the reader a good map to help them navigate it.