I would make Picard the living embodiment of a morally and culturally stagnant Federation and Riker a radical young officer who's constantly trying to change the world and to think outside the box. The show would be centered on those two never agreeing on anything but slowly building a respect for each other's abilities. In his quest to understand humanity, Data would question and test both of them. So the series would be built around the conflict between change and tradition, just like the original series was built around the conflict between logic and emotions.
Worf would be a prisoner of war turned collaborator. The others would be recurring characters.