One thing that served me well, I think, was ambition. Even before I went to college, when I was first falling in love with philosophy, my goal was to solve it. I wanted my worldview to make sense, dammit, and not be full of contradictions and incoherencies and "we don't ask that question" moments. Most of the philosophers regarded as great (Leibniz, Russell, Lewis, etc.) were grand systematizers who attempted to have an answer to everything, and were not satisfied with paradoxes/contradictions/incoherencies/articles-of-faith anywhere. Alas, no one so far has been able to succeed at this ambition, but nevertheless I think I learned so much more, and came to beliefs that are so much better, because of it.
Why? Well, one reason (though probably not the only reason) is that it helped me prioritize. It helped me move on from interesting-but-not-that-important puzzles and go for the Big Questions. And go straight for the throat instead of lollygagging.
The experience of trying to construct a coherent, non-contradictory complete worldview, only to encounter some new problem or puzzle that brings it crashing down, repeatedly is perhaps analogous to the experience of trying to construct a hypothesis about how celestial bodies move, or how optics works, or something, that can accurately predict all the data from all your experiments.
Formal debate is really really terrible in practice as a way to train anything resembling good philosophy, or else I'd think that a pretty good suggestion.
Specifically, all forms of debate devolve into speed-talking contests, because if you make a point that your opponent doesn't oppose, then they're considered by the judges to have conceded that point; so you want to make as many points as humanly possible in the time allotted. Aside from that, the game is all about coming up with clever argumentative maneuvers that have little to do with what arguments would work in real life and nothing al all to do with the truth.
Multiple attempted reforms of debate rules to get around these problems have failed, producing essentially the same result.
With respect to the distinct skills in "philosophy" -- I'm not so sure. I think maybe philosophy has correctly divided itself into subfields such as ontology, ethics, and epistemology. These subfields address different sets of questions, but use similar/identical "philosophical method" in doing so. This suggests that a common set of skills are involved in many philosophical pursuits, somewhat unlike the sports analogy.
Granted, I do suspect that there's a list of skills, which might best be trained separately. Here is an attempt to list what they might be:
The above three skills seem to be a bit overly anchored to a specific way of doing philosophy for my taste, but there you have it.