... I don't see a reason to make a wall hanger unless you want a wallhanger. Age has nothing to do with it.
+1. Nothing wrong with a wall hanger, if that's what you want. But that's not what I'd want.
If you want something simple, like a fixed gear bike, one from the 1890's should be just as ridable as a new one, though I would be concerned about wearing out irreplaceable parts.
With that in mind, I'd be curious: what's the oldest bike on which there are no irreplaceable parts? That is, no components that cannot be replaced with something that's still made?