IMO, the choice of firearm(s) for your wife comes down to a single question: Is she looking to concealed-carry?
If not and she's just looking for home defense, my opinion is to look into a 12- or 20-gauge pump shotgun. The manual of arms is relatively easy. Practicing on flying clays is fun for most every woman I've ever met. Practice ammo (birdshot) is plentiful. Defensive ammo is worderfully effective.
A lot of folks will say that the kick will be tough on such a petite woman, but there are add-on recoil-reducing buttstocks available that soak it up nicely. Another way to cut the recoil is to go with a semi-auto shotgun, but they're generally more expensive, finicky, and prone to malfunctions.
If she *is* looking to ccw, my suggestion is definitely to go to a range that rents pistols so she can try on a bunch of different models so she can find one that fits and she can control.
My opinion on pistols is that, in terms of stopping power, handgun rounds suck compared to rifle and shotgun rounds. At 9mm and above with quality ammo, it comes down to shot placement, not the size of the bullet. Find a pistol/caliber combo that she can conceal effectively, deploy quickly, and control precisely. Please note that the bolded items above are always a compromise. Small, light, easy to conceal pistols, for example, are usually wonderful to carry all day long, but more difficult to shoot precisely due to a shorter sight radius and a more severe felt recoil.
My problem with a shotgun as your only home defense weapon is that you probably won’t have it when you need it. When your doorbell rings at 4 in the afternoon, is she going to grab the 12 GA before answering, only to find it’s a girl scout selling cookies? Or carry it around out in the yard? A small snubby can be slipped into the pocket and carried without any problem or anyone knowing. A 12 GA doesn’t do any good if it’s in your bedroom closet when you need it.