There is not a list of best potatoes grown in Minnesota. You will need to obtain potato tubers from a reputable source, such as a greenhouse, versus using sprouted potatos from the grocery store. When growing in a box you may need to add additional soil in the early season. As sprouts appear you will need to mound soil around them as the potatos sprout off of the stems coming from the main tuber. Continue mounding the soil around the soil the sprouts for the first month for the greatest yield. Below I have attached a link for an article on growing potatoes that you may find helpful. http://www.extension.umn.edu/garden/yard-garden/vegetables/growing-potatoes-in-minnesota-home-gardens/