How should you choose a first portfolio project for a new skill?

There is a difference between saying that you have learned a skill and showing what you can do with it. A useful first project does not need to be large. It should address a real need, be achievable and make your decisions visible.

How would you help a beginner choose a first project? What should a strong portfolio explain: the process, the outcome, the obstacles, the feedback or the next iteration? Share examples from your own learning journey.