A suggestion: don't get too optimistic because I can probably watch 5 hours of TV a week max and at least 4 of them better be something my wife will tolerate. We've watched some crazy stupid bad anime lately. I'll also say that I'm a fan of anime, but a lot of anime is pure shit. Don't pick a pure shit one.
I feel the exact same way. I typically go by the three episode rule, if I think it's trash after 3 episodes I drop it. This kinda creates a problem.. I want to pick a series I haven't watched, and I can't pick one that's too long. So I guess that means we need guidelines, or to run multiple viewings. I know there are GREAT anime, but they are 70+ episodes. It's hard finding amazing content with a 12-25 episode range.
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.