Let me speak as someone who grew up in a rural area where hunting is a way of life, and consequently firearms are common.
The first myth of guns is that they are primarily for shooting bad guys. This is bogus, even in post-apocalyptic worlds. The thing that guns are used for more than anything is hunting, now and always (unless all the animals are dead in your world). And for hunting, pistols and machine guns are garbage. There are basically three types of guns used for hunting, which are rifles, shotguns, and muzzleloaders. The latter is basically a legacy gun, and is strictly inferior to the other two. However, in a post-apocalyptic world, the muzzleloader is probably slightly easier to get ammunition for (it's just a metal ball sitting on some explosive powder). Realistically, I think all of these guns would see continued use in such a world, because (1) there are good do-it-yourself reloading kits for rifles and shotgun shells in widespread use already, and (2) there are gazillions of rounds sitting in farmhouse basements all over the country.
Now as to the shooting bad guys business, it sounds like it's definitely going to happen in your world. But it's not going to be trench warfare, or even guerrilla warfare, so most of the "fancy" weapons that are used by modern militaries won't be very useful. E.g. machine guns are handy if you want to clear a battlefield (I guess), but if you're fighting in rugged country with lots of cover, you're way better off with a standard rifle. This is basically the same reason why bolt-action rifles are the preferred weapon for big game hunting--you benefit nothing from being able to fire rounds quickly, it spooks your prey, and if your prey is hunting you back it also gives away your position. Plus you waste rounds by firing quickly.
Again, I think we can learn about self defense by looking at what hunters use. In bear country, many people will carry a revolver or something "just in case" they need to gun down a bear, but in actuality nobody ever does. The best defense is bear spray (pepper spray). There are several reasons for this, including that we don't usually want to kill bears if we can avoid it, but also bear spray is effective even if you don't aim it perfectly (area effect). On the contrary, if you miss with a revolver, you still have an angry bear coming at you. The same could be said for fighting humans: If you are in a close enough fighting environment that a rifle is ineffective, then you typically will be better off firing pepper spray at your opponent first to incapacitate them (something like a taser could also be effective). After they're down, you could imagine a pistol being useful for "finishing them off" if you like, but there's a good argument that it shouldn't be your primary weapon.
There is one other element that's relevant for self-defense, which is intimidation. Scary looking guns probably make bad guys less likely to mess with you. However, for this purpose, it doesn't even matter if they are loaded. But it could be helpful to have a big gun to brandish when the marauders come by your farmstead, to encourage them to just keep on a-riding.
As a final comment before I conclude, let me point out that a post-apocalyptic world will not be a regression to the Wild West days, because modern knowledge will not be lost. People will still know the chemistry to make stuff like bear spray, explosives, and poisons, and some of it will be possible to make with only primitive ingredients. Similarly, the tools for e.g. reloading rifle shells will continue to exist and function essentially forever, and it's not difficult to fashion a new one if needed either.
So, in conclusion, what I argue would be the best armory for a post-apocalyptic world would be:
- Rifles, shotguns, and/or muzzleloaders. Exactly which you would choose depends on details of your situation. E.g. if you're a nomad living out of a backpack, then you'd probably want a muzzleloader, because it's relatively easy to get ammunition. If you were based in a farmhouse where you can set up a reloading station, rifles and shotguns are better. It probably doesn't matter which specific make of gun you go with, but if I had to choose I'd personally go with a 12 gauge shotgun, on account of being pretty universal and versatile, and something like a .30-06 or .308 rifle for precision shooting. All of these meet the criteria posed in the OP for being common, reliable, and easy to maintain.
- Some chemical self defense weapon like bear spray, or a taser (assuming you can charge it). A pistol would also be helpful, but it's for a more specialized purpose, and you wouldn't need to use it often.
Also, you asked specifically for guns, but modern crossbows are every bit as lethal, and you can reuse the bolts. So I would definitely have a crossbow in my armory, and that would probably be my go-to weapon for big game hunting if bullets were in short supply.
Edit: I see several other answers advocating primitive weapons. This is farcical. Humans haven't used spears or slings seriously in thousands of years. A modern compound bow will last a lifetime and be orders of magnitude more effective at both hunting and self defense than primitive weapons. Even if you had to fashion a bow yourself, using modern designs you'd be way ahead of spears and slings. See also my crossbow comment above.