Where does the lady in question live? Apartment, house/duplex? In town or the country? Next, can she own a dog? Are food and vet bills affordable? If she can, I'd check on getting a guard dog. The firearm after that. And I would suggest a handgun over a long gun. Can't keep a double barrel in your purse and there's gaurantee she'll only need it INSIDE the home.
As for the action, I suggest DA revolver. Several reasons, there's no way to accidentally release a cylinder. With an auto loader, if it gets dropped or the release button is hit somehow, your left with a single shot at best. Then there is the matter of malfunctions such as failure to eject properly or a jam. Revolvers don't have those issues.
As for the caliber of said revolver...I'd go with the largest size she is comfortable handling.