[Iwatasan]

You'd also want to make sure there's no chance the basement could flood in some kind of freak storm or whatever.

I haven't looked into this much myself yet but what about cabinets with glass/plexiglass/etc doors on the front to keep out the kids and cats? You could set up in your office and not worry about moisture issues in the basement.

If your particular basement isn't prone to those kinds of issues though, go for that. Put a TV in there and make it a gaming room. A video game collection would make more sense in a game room than an office probably.

Super jealous by the way, can't wait to have my own house for this purpose specifically.