Since you mentioned the wife using it, and assuming she isn't particularly proficient with a firearm I would go with a shotgun since they don't require the same proficiency as a pistol or carbine to be effective. That said, using a shotty isn't a reasonable excuse for not taking it to the range to work on the basic principals of marksmanship and weapons handling; safety manipulation; front sight focus and squeezing the trigger without disturbing the sights; shot placement to include body armor drills; loading and unloading; and failure (to load, fire, extract, and eject) drills to name a few.
With that, I would suggest a Moss 590/rem870 with an extended magazine and ghost sights for ease of use and reliability. I alternate slugs and 00-buck in the shotty HH6 uses when I am not present. That said don't neglect working a pistol in as well. If you are concerned about home defense you should also think about defense outside the home.
Also, if you haven't and with you just asking about a weapon it's a safe assumption to say you haven't, you should work on fall back hard points within the house; battle drills if forced entry is made into your home with/without you present; and what to [not] say to LE if she is involved in a home defense shooting - don't forget your right to remain silent in order to think about what is being said instead of just blurting out info. Poor wording, even in a stressful moment can be taken the wrong way. There are plenty of LEOs here who can steer you the right direction.
Lastly, I want to hit on mindset. There are plenty of books and other publications that talk about this but it bears mentioning. It's one thing to be physically prepared to defend ones own life by taking someone else's it's entirely another thing to mentally be prepared to do so. There are plenty of instances where LE and soldiers, hoping the other guy would do the right thing have waited too long and it cost their life instead - don't be that person. You are taking a big step in being responsible for your own security but make sure your mind is as dedicated to it on the inside.
Let me know if you want more info on any of the above...