Some thoughts to share.
If the world is going to Hell, I see no good reason to leave my house where I have all of my stuff. Any other place will probably have a lot of others milling about in desperation. How you decide to provide for your survival will focus on food, water, hygiene, heat etc. Guns will be but one very small part of what you will need to consider and deal with.
To come up with a scenario where picking out a gun for survival, you may think of being in a plane that went down on a hunting trip or similar where you are far away from civilization and need to survive. Use your imagination as it is a fun exercise. A good book about a boy with a hatchet in Alaska comes to mind. What most all of these scenarios will have in common is a need to survive with what you can carry as you make your way back to civilization. Please consider all you may want to have to carry, and in doing so, you may find you can only have one gun to do all you need. I guess if you are where Brown Bears live, you may want a shotgun as your first choice, some slugs and some bird shot would make sense. And a shotgun as an only gun for getting game and protection does make a lot of sense. If no lions and tigers and bears, oh my, you could also make do with a .22 and the way I shoot, it would need to be a rifle. On that note, I had a gunsmith line the barrel of a Remington 521T with a 1:8 twist liner. I can shoot the 60 gr. Aguila rounds accurately and those have enough sectional density to reliably pass through the lungs of a deer at reasonable ranges. That would be a comfort to have, light weight, reliable and adequate. Maybe an ultimate gun would be a .22 over .410 with the .22 barrel having the 1:8 twist.