Let me preclude this by saying I am not a professional trainer, medical practitioner or specialist of any kind.
However, I am in my 40's and was (20 years ago) qualified physical training instructor with the Canadian Military.
I am well read, and have trained in one aspect or another for the entirety of my life... most recently becoming more focused towards powerlifting.
For someone over the age of 55 who has been sedentary for the several decades... and has been medically cleared to begin a fitness/ training regime I would personally start them on some sort of aerobic/ anaerobic training regime- like circuit training of some sort.
This would get their blood flowing, lungs working and heart beating, also getting their sense of balance, flexibility and coordination in tune. It would also help them deal with muscle soreness and get some "good" endorphins pulsing through their system.
If possible, group them in pairs or even threes so that they share a common bond, can exchange their thoughts and feelings and in addition this will cause them to become more confident and comitted to the training as they will not want to let their workout partner(s) down.
This is just my opinion, and how I would tackle the situation...