I love my shotguns but if we are being objective (is that possible when discussing an apocalyptic fantasy?) then we have to admit that ammunition management is the drawback. Round capacity is limited, reloads are slow (vs. magazine-fed firearms) and while the types of ammunition that can be utilized are varied and multi-purpose try carrying all that ammunition around with you
For us city dwellers, the issue will not be hunting game during the first 3 months of the die-off, it will be other people coming to take what you have. Most scenarios paint a pretty grim picture after 3 days (72 hours). Remember the old rub; "3 minutes without oxygen, 3 hours without shelter, 3 days without water, and 3 weeks without food". Those are our practical limits for sustaining life.
So back to the city. Once power and the rule of law are both extinguished, the gangs, rapists, cannibals, cartels, etc., will dominate. Because our vehicles are no longer available, if you are planning to bug-in, you need at least 3 months of food and water (and coffee and toilet paper!). And most of all, you need a group.
You need lots of shooters! If you could see the thing coming (say it was mass civil unrest) and you could bug out (and had a place to go to), that's one thing. But with the EMP, you are stuck unless you have those bicycles with the little trailers like Abraham mentioned. So like TAM, I say you need lot's of guns and neighbors who are similarly trained and prepared. Fending off the criminals, the good people turned predator to save their children, the MS-13 gangbangers, the bad bikers, etc., will not be easy.
So I don't choose a shotty or a .22LR. And while I also love my 5.56 Colt SBR, that would only be my 2nd choice. My number one gun for the end of the world as we know it is my .308 SBR. Reach out and touch someone (cause I really don't want them to get too close, I much prefer a well constructed ambush or sniping from a few hundred yards) but if you have to go CQB, one round will pretty much end 'em. And the majority of light body armor will succumb as well.
I don't even have room to cache anything on this zero lot line property and my neighbors are mostly liberals. So after I clean out the duck pond, I may be coming for them unless they have something to offer that makes them worthy of joining our group. At least we have enough cars to barricade the cul-de-sac...