Depends if the reason was for Survival purposes, or because some liberal law said we could only have one of each. A hypothetical like this depends solely on the "WHY" can I only have one of each.
If it was because it was a law, then my choices would be:
1. Remington 870 12 gauge 3" magnum shotgun. Buy an 18" barrel for defense. Longer barrels for hunting bird, dear, etc...
2. S&W 357 magnum revolver. Able to shoot 38spl and 357 magnum. Able to be used for personal defense and hunting. Can plink without going bankrupt.
3. 7mm Magnum (Brand not as important). This caliber can hunt ANYTHING in North America. From prairie dogs to moose; from deer at 100 yards to big horn sheep at 400 yards.
If I was looking more at a survival situation, I would keep the same shotgun and pistol; (Remington 870 is pretty self explanatory; the S&W 357 magnum will be more reliable than semi-auto). But for rifle, I would have to probably go with a 22LR such as a remington or winchester. For survival purposes, I will need food. I can take a deer down with a 22LR, and NOT inform the entire world that I'm there. As well as rabbits, cats, dogs, squirrels, etc... In a survival environment, high power rifles are useless, unless that's all you have. Some might believe an AR or AK is a good survival weapon, but I can keep most human threats away with the 870 12 gauge or 357 magnum.
So again; only choosing 3 in such a hypothetical; is only productive if you qualify the "WHY". Fortunately, we live in a country that we aren't limited to how many guns. That's why I have my "3" collections of guns. 1) Historical: M1-Garand, 1862 Navy, 1903 Springfield, 1890's colt, etc... 2) Trading collection: Guns used specifically for trading. Usually I find a great deal on a weapon because someone needs cash, and I buy it. And may not personally want it, but I know I can turn it around in a trade towards something I do want. 3) My all purpose collection: Basically, 8 guns that I believe cover every possible scenario. So; if you're going to limit to 3 guns, it would help to know the reason why and what our environment will be.