The healthiest way to eat potatoes is with the skin intact, because that is where a fair amount of vitamins and minerals are. In terms of which type of potatoes have the most antioxidants, the rule of thumb to follow is the more colorful the potato, the more it has. Red potatoes rank right around the middle. When cooked, sweet and purple are most nutritious. White is the least nutritious.
ORAC Source
USDA Database for the Oxygen Radical Absorbance Capacity (ORAC) of Selected Foods, Release 2 - Prepared by Nutrient Data Laboratory, Beltsville Human Nutrition Research Center (BHNRC), Agricultural Research Service (ARS), U.S. Department of Agriculture (USDA) - May 2010