In my limited experience, shotguns are very versatile.
With a switch of ammo I can go from a gun that is perfectly suited to indoor defense (reduced recoil buck), outdoor defense (3" Federal full power 00 buck), or even knocking off the nearest big mean animal (slugs). If I had to I could even knock off something little and furry to eat with it.
The problems with a shotgun are that eventhough ammo is common, it is heavy. You can carry a couple rounds of .308 or maybe 4 rounds of 5.56 for one round of 12 gauge and what benefit do you gain from it? You can shoot a rabbit with it but shotguns are loud. It might not be a good idea if you can't afford to draw attention. A shotgun go from up close defense to killing a deer with a switch of ammo but a 5.56, 7.62x39, or .308 will work from point blank to 200 yards or so by just putting the sights on your target. A shotgun would give you the advantage that in the dark you would stand a better chance of hitting but what about the pellets that miss? They are going somewhere. Odds are that at some point law and order will be restored. Can you afford to just haphazardly send projectiles everwhere? The same thing would apply with a full power rifle cartridge on this one.
I am thinking that a 5.56mm has a lot of potential for the type of weapon that would be needed for this.
The rifles themselves are light and compact and if you go with an AR it can be dissassembled and reassembled in seconds. A folding stock AK would be pretty compact too.
The ammo is common and made in this country. Even if you are paying more for it, there was still lots of Federal, Winchester, and UMC 223 ammo around locally when 7.62x39 was nonexistent.
The ammo is light so you can carry more for the same amount of weight or carry less weight and the same amount of ammo. Or split the difference.
The 5.56 is occasionally critisized for difficulty penetrating barriers. In a SHTF, that may mean the difference between one of your misses not killing some innocent bystander where a shot from a larger round would have. If you need penetration you can switch to a mag full of SS109 and have a better chance, although from my understanding it will still not equal the penetration of a heavier round.
The round is generally more accurate than the 7.62x39 (at least the ones I have shot). This may be due to who is making the ammo, but that has been my experience.
Another factor for me is that not everyone in my family is well acquainted with guns. Even my dad, who has shot for over 50 years, would find my AR easier to handle than something heavier. He has degenerative arthritis in his shoulders and the lesser recoil is something he welcomes.
For my uses, my little Olympic AR may just be about perfect. I plan to put a compact 4x scope on it and get ahold of some heavier ammo and see what it will do.
A shorter barreled FAL might do too. With some careful load selection you can switch from something for an urban area to something that will shoot through some stuff. Mine is heavy though and that would be a factor when 2 pounds less of rifle means another quart of water.