Ok, I will play, working from the premise that order will be restored in a month or two, or the worst of the roaming gangs, etc. will kill each other off in about the same time frame.
1, Good quality light weight pellet gun to hunt small game, after all chances are the power is going to be out and there is no refrigeration (I live in the south). Even a .22 can be heard from a mile or more away, no reason to announce your location while putting dinner in the pot.
2, Ruger 10/22 in stainless, .22 LR because you can carry a lot of it, and when it comes down to it you can slow down a fairly large size gang at a fair distance with a .22, particularly if they are only armed with hand guns and don't know how to shoot.
3/4, A pair of larger caliber handgun / rifle that fire a common cartridge, something somewhat weatherproof and light. My personal choice at the moment would be an XDM-9 and a 9mm AR-15 conversion. If you need these chances are you were having to act in self defense, you either get away, or get more guns and ammo, or don't. I would be tempted to skip having the hand gun at all, and just go with a standard AR-15 or similar.
If we are talking about arming 2 or more people things change, if 2 people I would add a .22 handgun like the Ruger Camp Mk II or similar, and a second long gun like the 9mm AR-15.
It is all about not loading yourself down too much, and still maintaining a reasonable ammo supply, it helps if your not trying to roam long distance and can have a ammo/arms stash to go back to.