Well the obvious answer would be for you to watch the whole GitS canon. This means three movies and two seasons of the anime. The first two movies are very different from the show, but the third movie takes place right after the second season, even if the "changes" at the end of the season barely carry over.
Another cyberpunk classic is Akira. Everyone here will tell you the manga is better, but the movie is a landmark in animation.
As for just more serious anime in general that non-anime fans would be able to get into, Probably the top three shows ever made, in both my opinion and a lot of other people's are Mushishi, Planetes, and Monster. I'd look into those for sure.