My apologies for taking so long to get back to you Rickster. I have not been at my computer very much of late.
You mom is just a tiny bit older than I am. My mom and her sisters all are in various stages of osteoarthritis. My mom and her younger sister have been able to keep the more serious onset at bay with exercise. They both walk, swim and until my mom had knee surgery she lifted weights. After spending some time talking with my mom I learned it was her doctor that encouraged her to lift weights way back when she was first deemed 'at risk' because of her mother.
All weight bearing exercises will help your mom. Walking, swimming and weight training. If she's not accustomed to lifting she will need to start light, go easy and work her way into it. Training just three days a week will be beneficial for her in the long run. If balance is a problem at this point, machine work is fine.
Will she be training at home or in a gym? If she plans to train at home she can view vid clips at:
ExRx Exercise & Muscle Directory
I dug up a couple links that should be of help:
Arthritis and Exercise, How Do I Start?
Exercising with osteoarthritis
The Physician and Sportsmedicine: Exercise for Osteoarthritis