Coming to the topic way late and certainly just repeating what many have said...
Well, I mean, I pop in Shenmue: the Movie once in a while, so something along those lines would be neat. Side stories (maybe the ones we saw in the mangas, or something new) might be neat to flesh the world out further, although I'd miss the direct physical interaction/exploration and it wouldn't mean quite as much to me.
Alternatively, it would be pretty neat to have the stories of the games in concise, animated fashion. I think with 13 episodes they could pull off the important points of all three games (and if the episodes are longer, 30-60 minutes or something, for sure). II might need a little more, so maybe something like episodes 1-3 for Shenmue 1, 4-10 for II, and 10-13 for III.
And hey, anything that helps promote the series and push us toward IV/V.