I think 2 weeks with one discussion at the end of each would work best. That way, we only have to watch about 20 minutes a day to be on schedule. I think that is more manageable than the one week limit.
I agree with the movie idea. Most anime movies are pretty good quality, and a movie involves less time dedication than a full series. I remember this imgur album http://m.imgur.com/a/9UGCL from Reddit that had some good suggestions for movies that not everyone has seen, it might be a good place to start.