Here I give my personal reading approach to get familiar with the topics which the NuHAG is working on. This is just one way to get started, and I will mention some pros and cons I noticed. There is always some redundancy, but in my eyes that was of great worth.
A good way to get some first impressions is to read A Short Introduction to Gabor Analysis by Thomas Strohmer, which is the introductory chapter of [Feichtinger/Strohmer] and is also available online. You could also read the introductory chapters of [Blatter], which will make clear what the central ideas are in general. After having read that, you also want to understand it all.