What vitamins are best for keeping an elderly family member healthy?

All/none of them: It's a question of semantics. All vitamins are necessary regardless of age. Lack of various vitamins leads to specific diseases/conditions. For instance, osteoporosis is partly due to inadequate vitamin D. And some neuropathies are from lack of vitamin B12. Some anemias are due to lack of iron, folate and/or B12 (again!). Yet there are no studies showing any benefit from multipurpose multivitamin.