Tex (read "tek") is a program allowing to easily create (once you got a bit the hand of it!) great scientific documents for the use in academia. This is the best way to go for your PS: it will be cumbersome at the beginning, but it will save you plenty of time copying handwritten sheets.
For an idea on how to get started. you can read:
An Introduction to LaTex (video)
Downloading all necessary programs and installing them on your computer is one way to get ready to write. Hower, there are different online solutions that allow you to use it anywhere and even collaborate with your mates. Personally, I use Sharelatex, but Overleaf is also a pretty good alternative.
The books for the course, MWG and Gibbons, are sufficient to get the grasp of the issues treated in the course and have a quite complete preparation for the exam.
However, I sometimes used to read other material to get a better idea of some topics. Here it is a little list:
Game Theory: An Introduction, by Steve Tadelis
A course in Game Theory, by M. Osborne and A. Rubinstein (thougher than necessary)
The notes from J.Renault of TSE (really formal)
The series of videos from Game Theory 101
Anyway, these materials are not part of the course syllabus: they are not compulsory nor sufficient, moreover some of them are not of the same difficulty level as the course.
It is just stuff I found useful during my time in LMEc (I was a newbie too!).
If you are not convinced players are not fully rational... you are not alone!
Here something to read (if at all, after the end of the course) about this topic:
Ten Little Treasures of Game Theory and Ten Intuitive Contradictions
Behavioral Game Theory: Experiments in Strategic Interaction, by Colin F. Camerer