Setting particular makes aside, and thinking about caliber / effective range, etc., I have a proposal, just for the sake of argument. And I expect argument will ensue
The 12-gauge pump is a very versatile arm. With a rifled barrel and the right loads the effective range is out to about 150 yards. Considerably less if you are wanting a merciful kill on a deer, but as pointed out earlier, large game harvesting is probably not the best option in a survival situation. For the purposes of influencing an individual with ill intent, let's go with 150 yards.
The 5.56 has better range, say 200 yards?
But it seems to me they are in pretty much the same effective range. I'll call it medium range.
So, the 12-gauge will cover the medium range, plus has great versatility if you include both smooth and rifled barrels and a wide variety of loads. I say let's ditch the 5.56. (Them's fightin' words, rat there! Guys love their ARs!)
Plus, even during this current panic, with the gun cases and ammo shelves bare, there is still a pretty good selection of 12-gauge ammo to be had.
So I would propose:
1. OCrap range: pistol in caliber of your choice, always on your person, concealable
2. Medium range: 12-gauge pump (rifled barrel/proper loads)
3. .22 rifle for small game harvesting (in addition to the 12-gauge/smooth barrel/proper loads)
My fourth would be a a pistol-caliber carbine.
Justification:
Few of us are as good as we think we are with a pistol.
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For home / close up defense a carbine has a much better sight radius and longer barrel than a pistol; both of which increase accuracy. And a shorter barrel than a shotgun (16" v. 18"), making it slightly easier and quicker to maneuver in tight places. Plus IMHO a pistol caliber like 9mm isn't as likely to shoot through walls and stuff as either a 5.56 or 12-gauge. I have to leave the pistol on the list, though, since it isn't practical to keep a carbine on your person at all times, and nearly impossible to conceal.
If I had a five-gun rack, and especially if I lived in, or expected to be surviving in, the wide-open spaces, I would add a long range arm; a scoped 30-caliber rifle (.308, 30-30, 7mm, etc.). But probably not in place of any of the other four.