Your grandparents lived well into their nineties, and so did your parents, and as a healthy senior, you have expectations to do the same. Your children may not be in the best position to take care of you, though, and you do not want to be a burden if you suffer mobility or other health issues that run in your family. On the other hand, if you need long-term care once you reach your early eighties, it may take all your assets to cover your expenses for a decade.
Medicaid does cover many of the costs of living in a nursing home, but there is a maximum amount of assets and income allowable. As long as you make more than that amount, you will have to pay for your expenses yourself. Fortunately, you have estate planning options that will not deplete your family's inheritance.