But choosing a goal is an action in this sense, so there's eventually a recursion problem with choosing your own goals, unless there's some highest goal you hold which isn't chosen by you.

I can't fault your reasoning. So I'll limit it, instead.

In a broader sense of "choice" it is still possible to choose a highest level goal. To wit, you can try pursuing it, and find that you continue to do so, perhaps even more strongly than initially. Alternatively, you can find that you lose all interest. Over the long term as you try different pursuits and settle into a stable set, you can be said to have chosen your goals - just not in the explicit matching-means-to-ends kind of way.

"But this just amounts to choosing satisfying pursuits! So the highest goal is really satisfaction." OK, if you want to talk that way - but note that "satisfaction" may amount to nothing more than this very fact of goal stability in the face of experimentation and learning. One might as well say that your highest goal is to choose pursuits that are worthy for you. Come to think of it, that's exactly what I would say.