Well, not just physical form. Philosophical form too.
My first post elicited some great comments, and a few months of thinking have pushed me into a rough plan of what I want to do. Let's see if I can flesh it out here.
For the physical space, I will be filling four tall display cases. They're all 18" deep and 79" tall. two are 31" wide, two are 62" wide. I won't be figuring the exact physical layout today, but those are the parameters. There's also the possibility of placing a standup arcade machine outside the cases. Decent power is available in all the cabinets; networking, maybe.
First, I still like the three themes I originally thought of, but here's some elaboration.
Why are games fun? I will base this on a short explanation of the reward structure in all good games (how they make you feel challenged but not overwhelmed, and how they have a pleasurable reward structure).