Joeg,
There's nothing "wrong" with any of the suggestions listed so far.
I think the real question is, how much firearms experience has your wife had? You may be thinking "If there's a bump in the night, I'll be the one getting the gun and checking things out" but consider this... you have a friend coming over in the next few minutes, so when you hear a knock at the door you go to let him in... only it turns out it's not your friend, but a couple of thugs there to do a daylight "home invasion" robbery. One has a (pole, baseball bat, crowbar, whatever) and starts to wail on you right there at the door as they force their way inside. You're on the floor taking a heck of a beating - now, is your wife standing there in horror looking on, or is she running for the back room to get the gun? When she gets it, will she know what to do with it? (see if it's loaded, make sure a round is chambered, safety is off, etc) and once she gets it into action, will she be more likely - under STRESS - to get solid hits on the bad guys and make sure she doesn't shoot YOU or thru a wall and hit the neighbor kids in their sandbox? Will she still be standing after firing a 12 gauge full of 00 buckshot, or will she be falling backwards or thrown off so much by the blast and recoil that getting in any follow up shots is an "iffy" proposition?
My suggestion would be to get the largest manstopping caliber in a package that both you and your wife are both able and WILLING to go and practice 100 shots at least once every 90 days at your local range. If that is a 9mm, then fine. If either of you have hand strength issues, then maybe a revolver. I'd advise hitting a rental range and test-driving a few handguns if you are of a handgun mindset. The suggestion of a 20 gauge shotgun was pretty good. I like the 20 gauge with #4 buckshot, it seems to be the sweet spot in that gauge between penetration and pellet count. The M1 carbine is not a bad choice if they are ok in Jersey.
Regardless, your wife is your backup, and a backup with zero training and experience is just someone to call the ambulance for you after the fact.
Not wanting to criticize at all, just wanting to offer you some food for thought. Good luck in your search.