I would show them the 70th Anniversary Blu-ray of Casablanca.
[Show spoiler]
This restored transfer of Casablanca is a good example of how old movies no longer look like "old movies" when they are viewed in high definition, and it is a great example of how the world of Blu-ray elevates familiar well-loved movies to a new level so that we feel as through we are watching these movies for the first time all over again. I would then steer this person to the Blu-ray transfers of The Adventures of Robin Hood, King Kong (1933), North By Northwest, Bela Lugosi's Dracula, the Sean Connery James Bond films, Seven Samurai, and many others.
The best thing about Blu-ray is experiencing old movies that have been lovingly restored.
I've been trying to find that version for a good price since I started collecting.