Yes, definitely go for reconditioned. Even if stairs aren't straight, it's possible to have a bespoke rail and a reconditioned chair, which will still be a lot cheaper than new - this is what my father had. Fitting can be extremely quick, like less than a fortnight from commissioning.
I went for a locally based firm, who were very responsive and gave good service.
Whether it's worth doing depend on the specific case. My mother had one which she used for 10 or more years. My father used his for 3 months, but it delayed going into a nursing home for that length of time, and cost considerably less than nursing home fees.
Are your relatives suffering from general frailty or from dementia. The way of operating can be really easy - push the button in the direction you want to go - but, even so, can be difficult for a person with dementia to remember.
Finally - it's important to go up in one smooth go, not in fits and starts. There's a trigger point about 1m from the end to tell the chair to slow down. If you stop just before this then restart, the chair can fail to trigger, go full tilt into the buffers, and get itself jammed. No danger of injury, and your at the top (or bottom), so you're not stuck on the chair, but it won't work next time.
One thing to beware of - "24 hour call-out" - does this mean they will come out in the middle of the night, or does it merely mean you can call them in the middle of the night and they'll send someone in the morning?