I wonder if After Effects has an effect for this so I don't have to use an expression (as I am rather a beginner, I guess this would take me a lot of time...)
I have a title in mind (one word), where all the letters move around themselves, randomly but just a little, until they get into place. Like the letters were searching for their place (a metaphor for the film).
Does anyone have a tip for a way to achieve this?
Look in AE's text animation presets. There may be something useful under tha Animate In category.
Unfortunately, there is nothing like that...
There are several text animation presets that should get you close to the look you want.
You will just need to tweak them a bit to do what you want.