Nursing home really would be a last resort.
If you need nursing home care, then its not so much a last resort as a wonderful facility.
You should plan on the basis that you will be going into a nursing home at some future point. The only other possibility is that you will die before you need nursing home care.
How will this be funded. If you hold assets other than your home you will have to pay for it yourself, if you don't the state will pay for it.
Your question as to how what assets you should hold onto basically comes down to, do we keep enough to fund nursing home care ourselves or not.