I think the first rifle everyone should have is a small bore (like .22LR). Ammo is so cheap and plentiful and it's fun and easy to shoot. Lets you get in plenty of practice.
After that, I'd go with a 12-gauge and then .308 like MoBob said. Then you've got pretty much all bases covered.
If you really want to cover everything I would pick up a small frame pistol (either in .357 [which would shoot .38 as well] or 9mm) and a semi-automatic rifle in .223 or 7.62x39. But, that depends on the legalities in your area and how far you (and your wife) want to go.
On a side note: My paternal grandfather and my great-uncle on my mothers side (who never met each other) both chose a semi-auto .22LR and a smooth bore pump 12ga shotgun as their only firearms. Which I thought was very interesting.
After some questioning and thought, I figured out why. A shotgun loaded with slugs can take out deer at 50 yards pretty easily, can take out birds in the sky with bird shot, and if someone comes in your house unannounced, hearing that slide rack is enough to make most of them do an abrupt about-face.
The semi-auto .22 was more for shooting practice and varmint control, but it also was easy and fun for just about anyone to fire, from kids to the elderly. My grandmother used it quite a few times to get rid of small rodents tearing up her garden.
Therefore, between the two firearms they could take care of just about any normal task on their property. To them it had nothing to do with survival or bugging out, these were more or less just tools for use around their homes.
When I think about it, if I could only choose two I would choose the same they did, a semi-auto .22LR (like a Ruger 10/22) and a smooth bore pump 12ga shotgun in 2 3/4" or 3".
Now, if I could choose five, I would pick the .22LR, the shotgun, a good .308, a good pocket-able .357, and an AR or Mini-14.
After that, just for fun, a good .45 (probably a 1911), a lever action rifle in .357, and one of those awesome S&W .460 revolvers. But, that's just me.
err....I better stop before I get way off topic.