Fun hypothetical (I hope) question. If I'm picking one just to have and not think about all the use issues, it is my MAK-90. It is great for defense and I can press it into hunting use.
But really if I thought about all the things I want to do, I'd have to go for a reliable 12 ga. shotgun like a Remington 870 or Mossberg 500. It is more effective in home defense than a pistol when loaded with buckshot. Slugs hit hard and give me a good 100+ yard range for hunting/self defense. I can still load the gun with birdshot if I need to to hunt birds/small game to feed my family. Overall, I think shotgun is a jack of all trades, master of none gun. Its going to do a little of everything and if I had one gun I want it to do as many jobs as possible. Plus any place that carries ammo I bet they will carry 12 gauge shells so feeding it easy. They are propably the some of the last guns on most antigunners the ban list so I know I can have it until the very end if things go wrong politically.
I understand about having a handgun to conceal and take with you more places but I think the shotgun does more things so it makes it the better choice. Then I'd go for my Glock 26 if it had to be a handgun.
I guess the question is if you can have only one gun, or one thing that would register as a gun. I could see something like a Thompson Contender with many barrels or an AR with many uppers as an option. Would that be cheating?