I know quite a few folks belonging to one-gun households. The ones that are semi-rural/rural have a shotgun almost without exception. The ones who are more suburban/urban are usually handgun, though a fair number of scatterguns there, too.
The reason for the shotgun in more rural areas is obvious, and traces it's roots back to the days of the pioneers. While the Colt revolver and Winchester rifle got all the fame and glory, the shotgun was the real workhorse and is truly the gun that settled the west. Versatility was/is the name of the game if you can only afford/carry one firearm, and the shotgun has more of it than a handgun or rifle.
I only know one person who had a centerfire rifle as his only gun, and that was for about two weeks until he picked up a handgun.