# How could a single Python script run when Blender is started?

I would like to have a few globally available functions which should not not depend on a .blend file. Is there a place (A setup.py, __init__.py or something like that) where I could put a few lines of code?

As documented in the manual, you can save your script in the scripts/startup/ directory with a .py extension and it will be automatically imported on startup.
If it's per .blend file, then you can use Blender's Text Editor within that file, store your python commands there, and enable the Register checkbox in the Text Editor's header. The only caveat to this approach is that you'll need to start Blender with the -y flag so the embedded script will run on start.