I'll take a crack, although the problem is that you've got a number of somewhat contradictory criteria. If the question were simply best home defense gun, I'd be inclined to go with some kind of 12 gauge pump shotgun and OO buckshot, particularly since you live in a rural area, so over-penetration is less of an issue. Otherwise loaded with #1 #2 birdshot. Mossberg 500 or 590, or Remington 870 are your best bets.
Unfortunately, this is not the best choice if you wife also has to shoot, as recoil can be pretty stout. Also, not really a gun for target shooting, unless your targets are ripe watermellons about 10 yards away.
Getting an HK94 clone or similar semi-auto carbine type weapon that shoot a 9mm pistol round would be a fun, and tacticool alternative. You will be more accurate and better able to make follow up shots than with a pistol. Recoil will be light, so no problem for spouse. Will probably come with a 20 or 30 round mag, so you shouldn't have to worry about running out of ammo. And a lot of fun at the range. The problem is the cheap requirement. A real HK94 will cost you $2,500 or more. A clone, if you can find one, will still be about $1,000. Not sure what some of the other alternatives (I think Berreta makes something like this) will cost, but they won't be cheap.
Moving to handguns - larger calibers equal more stopping power, but also more recoil, which will make it tougher for spouse to shoot. Honestly, your best bet is probably a 9mm semi-auto, particularly since you plan to keep the gun unloaded and loading a revolver, in the dark, with an intruder trying to knock down your door, may be problematic. You have a lot of choices here. Glock 17 is a very popular, reliable and easy to operate choice. Sig 226 is a great gun, but will be on the pricey side. Berretta makes a nice gun. So does Springfield. And Smith & Wesson. Honestly, it's hard to go wrong unless you either cheap out and buy a no-name gun, or you choose something that's very small and very light, which will make it harder to shoot.
Finally, you could go with a semi-auto rifle of some kind. Ruger mini 14 might be a good choice for what you want. This would also make a great plinking gun if you wanted to go to the range. And could be operated by wife pretty easily.
Of course there's always an AR15, which would make a great plinking/range gun, but would probably not be the best choice for HD. Also going to be more $ than you want to spend.
Finally, you could go crazy and get a Garand, an AR10, or an FAL. But that assumes you plan to take out that pesky intruder while he's still a couple of hundred yards away from the house.
