If you hold to the rules, only one gun and the SHTF scenario and don't just pick your favorite gun, it's a worthwhile question.

I can see the advantages of a pistol but it would have to be a revolver with their reduced maintenance. They are light and you could also carry at all times.

If you're thinking of living off the land and not your neighbor, then I would lean towards a light weight 12 gauge pump. They can hunt birds to bears and require very little maintenance.

Things to not consider, no matter how cool they are, Semi-Auto's they require to much maintenance. I can't believe all the people who picked AR's. They are cool but I'm going to take your food when your guns don't work