My 70 year old mother has been talking about needing a gun for hd.  Now Mom isn't a frail woman by any means but she is 70 years old.  I'm willing to buy her whatever works but not sure what to get.  

She has zero experience shooting firearms and lives alone.  

thanks for any advice

If she can handle a shotgun get that. If not a revolver in a smaller caliber.

.38 revolver

Colt small frame

I am going to go against tradition and suggest a pistol caliber carbine, something light and compact. Teach her how to use it. Has the ability to mount optics/lasers/lights. If you put an optic, I would recommend something fiberoptic w/tritium.

That's my outside the box thinking.

A long gun will be a better idea than a pistol or revolver. I would recommend a PCC or an AR.

A super lightweight AR with a red dot.

I'd take her to a trusted gun store with a range.  At a good store, the staff should go out of their way to help her find a weapon that works for her.  I'd buy her a session or two of training with that gun at the same time if you aren't confident/qualified to teach her, or if you think she'd feel more confident with someone else (i.e., a "professional" may not have more experience but she might believe they are, and that might make all the difference).

For my mom? The best fit would probably be a reasonably lightweight 20 ga auto with a correctly fitted, recoil reducing stock, 18" barrel, a slightly extended mag tube (same capacity as a revolver), and a slightly large fibre optic front bead to make it easy to aim accurately.  I know some people hate the idea of a shotgun as a home defense weapon, but they are easy to understand and use.