what would they be? As Kim said, if someone says you can only have one, you shoot the bastard. This is a little different. If you could only have a few, having to bug out or whatever, what would be the minimum you'd want?
I figure five, broken down as follows with some notes at the end:
A centerfire rifle. What caliber would depend on what your primary perceived need would be and what part of the country. Primarily a combat arm, a semi-auto would be better; primarily hunting, another action type would be as good or better.(a)
A rimfire rifle. Ammo is cheap, which means you could carry a lot for little cost and weight. For hunting or varmint control you get accuracy with low noise and recoil, and long term it gives a way to practice without using the heavy stuff.(b)
A centerfire pistol. This could serve both for defensive use and, depending on type/caliber, hunting use.(c)
A rimfire pistol. Same reasons as the rimfire rifle. And, if you're with someone who can't handle something heavier, it beats nothing for a defensive arm.(d)
And last, a shotgun. This is, probably, the most versitile arm you could have. With birdshot take small game; with buckshot and slugs large game; and with all of them it's a serious defensive weapon.(e)
With this combination, you'd be able to take care of just about any problem to arise.
(a) Type, of course, depends on use, caliber is much more subjective. A combat arm could be done in .223, or .308, or 7.62x39. But if you're also/instead thinking of hunting, it gets more complicated. Over much of the country a .30-30 would work fine(as well as easy ammo availability), or an old 6.5x55 Mauser, but if you live in a place where shots might be longer or you might have to deal with bears/moose/elk, a heavier cartridge would get the nod. I remember once reading of a man who was setting up a moose hunt, and when he told the guide he was bringing a .375 H&H Magnum, the guide almost teared up at someone bringing a cartridge he could trust as heavy enough. Yeah, a .308 will take just about anything if the shot is perfect and if you can do it under whatever conditions; however, most of us don't have the shooting skill and nerves under stress of W.D.M. Bell.
(b) The main contenders here would be the .22LR, the .22 Magnum, and the .17 Hornady. All will work; the magnum and .17 will give longer effective range. The .22LR has the advantage of being able to use shorts(the others can't) which can be very quiet and effective on small game up close.
(c) Pick your main use and choose caliber from that. While a semi-auto is generally better defensively, there's not a thing wrong with a good revolver.
(d) See (b). One nice thing here is that some revolvers come with two cylinders, .22LR and .22 Mag, so they have a bit more versatility; the mag cylinder can make it a nasty defensive arm.
I'll note that you could combine the centerfire and rimfire pistols by having a semi-auto centerfire and a .22 conversion for it.
(e) Semi-auto or pump or double or single-shot or bolt, in a fight no handgun ever made can equal the close-range stopping power of a shotgun. With buckshot or slugs the range reaches out further, with some shotguns with rifled barrels and the right slugs giving rifle-level accuracy out beyond 100 yards. As long as you work within the range of your piece, you can take any game animal in North America(and many other places) with one, and with practice a pump can throw shots about as fast as a semi-auto.
There's my selections as to type. For particulars, I'll be adding that later. This'll take some thought.