I think the answers will vary, a little, based on the population density of their home. If your family is in the city I see no need for the high-powered big game rifle, unless you live in Anchorage. Few of your shots are going to be over 100 yards, if that. And if Bambi's Mom does wander through, the shotgun should be more than enough-we'll make sure Family X gets some a case of slugs. too. For most of the other tasty critters that live there the rimfire will be sufficient. Country folk, OTOH, are advised to get such a rifle, since: 1. Large game is a much more likely possibility, and 2. Wide expanses of field and meadow will require your big cartridge and quality scope, should you have any need to target any sort of creature at a distance.
Ridge Runner's NEF idea is a good one, but another, less expensive option is a second shotgun, a break-open (SS, O/U, or SxS), and a few sets of shell adapters. You never know if you'll find shells while rummaging somewhere, but isn't good to know you'll be able to use that 16/20/28/.410 in your 12 gauge?
For a battle rifle, well, I think a semi-auto rifle is good. Sometimes quantity of shots will be more crucial than quality, although not often.
I'd be quite satisfied with an SKS; robust, fairly accurate, inexpensive, and ammo is fairly common. A semi-auto AK-47 is good, too, as long as you have the discipline not to Rambo away that 30-rd magazine. I don't think our family is going to need something in the AR/FAL category, since the odds of making an offensive is near zero. Family X (and their neighbors, Y, Z, A, and B) are going to be defensive. Rural Family X might find battle rifles that have a longer field of fire a useful addition, however.
Revolver or semi? Whichever you're more comfortable with. Stick to common but potent calibers- 357/38, .45, .44, 9X19. I have nothing but praise for the Makarov, too, but finding 9X18 or even .380 is going to be tough once my cache is empty.
Twenty-twos? A bolt, lever, or pump action are my first choices-again, less risk of Rambo-ing out. You need to lay cover for some reason? that 22 semiauto pistol will keep their heads down as good as the rifle will. And an accurate 22 rifle is going to put critters in your pot, and you want to get used to the idea of conserving ammo. It's way too easy to keep pulling the trigger until you're out; pump, lever, and bolt require an additional action to shoot again. One can still go to near-zombie with those, too, but it's less likely.
And since Family X is starting from scratch, I want the whole family to take a safe handling class, and I want the adults to have some kind of tactical shooting classes, so that if they need to shoot, they don't do more harm than good. I'd want the kids to know how to shoot, although I have strong reservations about teaching a child how to shoot a person from any farther than across the room (If her life is in immediate danger, that is one thing; being able to pick off the enemy at 200 yards is quite another [although I'd be very proud to see her hit the X-ring on a target at that distance, too!]).
I won't recommend specific name brands, because the most important consideration is that each member of Family X is comfortable with. I love the SKS, am neutral on the AK, and loathed the AR. YMMV.
