I have a lot of customers looking for the one gun that will do everything they'll ever need. As most of my readers know, that's impossible. You can get away with limiting yourself to as few as two guns if you choose the right ones and do things in specific ways, but most gun people would recommend at least three, preferably the rifle-handgun-shotgun trifecta. This does leave out the .22 most would suggest, but we're talking minimums here.
Depending on your personal view, there are two ways to go with this--concentrate on one readily available caliber in each category, or attempt to have a wide range to prepare for as many possible options as you can. Since we're talking minimums, we'll go ahead and talk readily available.
For a single rifle to do what you'll want for both hunting and SHTF situations (and, actually, hunting IN SHTF situations), semi-automatic is preferred, especially if higher-capacity mags are available, as opposed to hunting magazines. Most people will choose .308, .223, or 7.62x39. Depending on your state, the .223 may very well be illegal for hunting, but that's alright if you won't be hunting until the SHTF situations; it'll do, as long as you know what you're doing. 7.62 is probably the most affordable rifle, since the SKS and AK are both readily available at reasonable prices. There's also a lot of ammo out there for it. The AR platform, though, is probably the platform of choice due to its weight, readily available parts, and widespread use in police and military agencies. The .308 is also commonly used, but will be the most expensive option (it's also the most practical choice for a hunting/battle rifle, since it will work very well for both purposes).
Since we're talking about the guy who simply wants one gun, they probably want to save money. Let's find them something in an AK. WASRs are commonly available and cheap, but probably not the quality I'd recommend. Saigas, on the other hand, are also cheap, and they can be quickly adapted to accept AK mags. They are also some of the better ones out there (though the AK accessories and pistol grips aren't usable without serious modifications, the Saiga that can accept AK mags should very easily suffice).
As for the shotgun, we don't have to get too fancy. It's mostly for home defense or close combat and good for some hunting. I'd recommend something simple, like a Remington 870 or a Mossberg 500/590/835. A short barrel is great for defensive use, while you may want a longer barrel for hunting. If you want to get fancy, you can get something like the Benelli M3.
A suggestion here: the 870 is going to have the most widely available parts, and you can often pick up a used one for a pretty decent price.
The handgun is going to be a sidearm. You will want it for carry, and it'll do just fine for home defense as well (this is how you cut yourself down to two--cut out the shotgun). You will want something in a common caliber, reliable, and accurate. You also want it to be something you will actually carry. That Desert Eagle may look badass, but even the .357 or .44 versions will be heavy (and notoriously unreliable), and the .50 AE is going to be a pain to find. 9mm, .40, and .45 will be great choices, and .357 will be your best choice for a revolver. Some of you might be saying that you'd prefer a Five Seven, since it is incredibly light, very accurate, and has the best capacity you'll find. It is a good choice, except for the ammo concerns. Your best bet is a Glock (though I loathe them so), a Springfield XD, or a Smith & Wesson M&P. Personally, I like .45, so I generally carry an XD or a 1911. The XD is probably your better bet, carrying 13 rounds (as will the Glock 21), giving you quite a bit of firepower with only a couple mags. The new XD-M is probably going to be the best bet for most people, as .40 is incredibly popular among police agencies, and it has 16-round mags.
Something to think about here--9mm is in common use in the military, and .40 is probably the most common police round. In a SHTF situation, there are two things that could happen--most available ammo in those calibers goes to those agencies, leaving very little, or you can end up acquiring ammo from these groups, increasing your supplies.
If we've got a cheapskate trying to get all set up here, there's probably a Saiga, an 870, and a Taurus (although there was a Glock 21 that looked almost unfired pretty cheap at work the other day, so maybe there could be an upgrade on that front). That's a respectable trio, and a good start. Make sure to stock up on ammo.
Another consideration is whether you'll be with others in a SHTF situation. If you will, you may want to talk to them about the plan. If you all bring ARs, you can share ammo and parts. If you bring a long-range weapon and others bring shorter-range rifles, you'll play different roles. On the other hand, if you will likely be alone, that single-shot .50 BMG really won't be as much help as a high-capacity AR.
My choices are a Remington 7400 in .30-06 and a Saiga 7.62x39 (I keep thinking I'll add an AR, but I don't really want to spend that much to add another caliber). I also have Mausers in 8mm and Enfields in .303, so I have some bolt guns that would probably end up as my hunting rifles if the SHTF. I have a Mossberg 835 and a single shot Survivor in 12 ga. I have some .45s and a .44, and I'm going to be picking up a .40 (the XD-M). I also have some .22 rifles, so I'm fairly well-set. Unfortunately, I'm low on .303 ammo right now, but that isn't something I should be relying on in a SHTF situation. I also have the equipment, powder, and bullets to reload in .45, .44, .30-06, and 8mm Mauser.
Over at TSLRF, Ryan has (or had, as he may've changed his mind since then) a different take, I see. He says you can cut out the rifle. It's true, but I wouldn't. The rifle plays an important role, since the shotgun won't have the capacity and neither the pistol nor the shotgun will have the range. In any case, no one firearm can truly fill all the necessary roles.