Great idea, OP! My DS sounds a bit like yours. Instead of movies, we usually binged TV shows together. It was nice because, since they were of shorter duration than movies, we could easily start/stop them. We also had a pact that we had to watch them together - no going off and watching by yourself. I focused on finding shows that he was unlikely to have seen before such as:
Warehouse 13
Grimm
Star Trek (all iterations)
Breaking Bad
Star Wars animated series
Last Airbender (original cartoon series - we later watched the movie and discussed)
X-files
On a side note, we used to do a regular family Classic Move Night (kids are in college so not so regular anymore). When I first made the pronouncement, the kids weren't that keen but I, of course, knew what amazing movies there were that had been made before they were born and selected GREAT ones. Later selections included those everyone needs to watch at least once - like Casablanca, The Good, The Bad and The Ugly, Singing in the Rain, etc. One of our favorites (if you don't mind the language) is the original Bad News Bears.