Some general thoughts for the OP. I start with the assumption that your mother is a novice handgunner, otherwise she would know exactly what she wants already :-)
1) First, I second DocRocket's thoughts about letting her try a few handguns to see what she likes best. And best means not only what she shoots best, but what she feels most comfortable with in terms of "administrative handling," i.e. loading, unloading and manipulating the firearm, the safety, if any, etc..
2) An intermediate size, weight and power handgun is probably the best bet. Too light is hard to hold steady especially when adrenalin kicks in, and too heavy is, well, too heavy. Also, a light handgun kicks more - .38 Special +P in an alloy frame revolver can have a sharp, uncomfortable recoil especially in arthritic hands, and a couple of cylinders of .357 Magnum in a Ruger SP101 steel frame revolver will more than satisfy many a novice shooter's recoil quota for the day. A small, short sight radius is difficult to shoot accurately and a long sight radius is harder for old eyes to see both front and rear sight relatively well - one reason why older target shooters often prefer shorter barrel lengths in their target guns.
3) A swing-out cylinder double action revolver is the easiest and simplest for loading and unloading, making sure the firearm is unloaded, etc., which can make it the best choice for a "non-dedicated user" who doesn't want to spend the time and practice to make the more complex manual of arms of a semi-auto reflexive. On the other hand, the relatively stiff double action trigger pull may be difficult for arthritic hands to shoot well. Of course a double action revolver can also be fired single action, which gives a nice, light trigger pull, but if the need for shooting passes, one has to decock the hammer.
4) A single-action semi-auto (e.g. Colt 1911 pattern or Browning Hi-Power) is easiest to shoot well but has a more complex manual of arms and the slide can be difficult to manipulate for loading and unloading for someone with hand arthritis and decreased hand grasp strength.
5) A semi-auto with external hammer is easier to manipulate the slide than a striker-fired semi-auto because you can first cock the hammer before jacking the slide. Obviously this should always be done while pointing the handgun in a safe direction in case the hammer should slip, and a firing-pin block such as the Colt Series 80 model has is a nice additional safety feature if this procedure is done on a regular basis.
All of these factors need to be considered when choosing a suitable handgun, in addition to how well it shoots, which is why it is important for the prospective owner (your mother) to try them for herself.
