For the last part of the Computer Lab Box I wanted to have the possibility to make a net boot provided by the main computer. This was a very easy task. I found already before a good tutorial on https://bootlin.com/doc/training/linux-kernel/.
For now, I am using a cheap USB memory stick as data storage. Later I want to buy an external SSD.
I also updated my main computer from a Raspberry Pi 3 to a 3+.
The last task is to make a clean image and to install only the needed and tested scripts and tools.