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.