How should whole raw potatoes be stored?

Store potatoes in a cool, dark, well ventilated area where there is little, if any, direct sunlight. Storing potatoes in excessive sunlight causes the skin and flesh to turn green. Green skins are toxic, and green flesh tastes bitter. 

The ideal temperature for storing  raw potatoes is ~55°F (just below the soil temperature at which most  plants germinate), which is often the temperature in a basement or crawl space. If you don't have a spot at about that temperature in your home or apartment, if you have to choose between room temperature and refrigeration, storing in the refrigerator will allow potatoes to last longer without spoiling inside. (However, they won’t keep as long as they would if kept at ~55°F.) In general, potatoes will keep for 1-3 weeks in the refrigerator, but this depends on when they were harvested before they got to you.  Starch conversion to sugar is constant in tubers, but it becomes more rapid below 50°F.  High degrees of starch-to-sugar conversion cause the potatoes to become “mealy."
Sweet potatoes should be stored the same way as white potatoes. The usual advice is not to refrigerate them, but they will tolerate refrigeration as long as they have been “cured” at 85°F for 5-8 days to allow the skins to dry out and harden.

Raw whole potatoes can be stored wrapped or unwrapped.  If wrapped, they should be loosely wrapped or wrapped in perforated material.
Do not wash potatoes prior to storing them. Residual moisture will accelerate spoilage and mold growth.
 Source(s):
Susan Brewer, Ph.D. University of Illinois, Department of Food Science and Human Nutrition