Thanks for the input everybody! We're going to size up a few pump shotguns and even a few pistols this weekend.
In this case my vote goes to a hands down easy to manage gun. In that arena for HD, nothing beats an M1 Carbine. They're short, very light, have almost no recoil, the bolt is very easy to retract, the trigger is very manageable, the capacity is generous (15+) and it packs a punch equivalent to a .357mag. You can choose to store it with an empty chamber with the safety off, or a loaded chamber with the safety on. Making it ready to fire will be no more difficult than any other gun a person with a small build or infirmities (even future infirmities) could manage.
As for their budget, what about yours? If they're your loved ones (or someone loved by someone you love), it's a good deed to help set them up. The gun will come back to you eventually, and the positive effect you generate will be very much appreciated. I don't have very many loved ones in my life any more, but for those that remain, my gun safe is open for their needs. Just a thought.