When choosing potatoes, always look for firm, fresh specimens with a smooth, unblemished skin. Avoid any that are soft and rubbery, that have green or mouldy patches, holes or sprouting eyes. Green patches are caused by exposure to light and indicate that the potato contains an abnormally high level of solanine - a poisonous substance that is not destroyed by cooking. If you discover green patches when peeling your potatoes, the only thing to do is chuck them out.
I generally prefer to purchase my potatoes loose from a greengrocer. Pre-washed potatoes are more likely to spoil quickly than unwashed ones, especially when wrapped in plastic. So although the plastic bags of washed potatoes sold by supermarkets seem convenient, they are really only worth buying if you plan to use them within a couple of days. They are also more expensive than loose potatoes. When buying unwashed potatoes, make sure the soil on them is fresh; if it is slimy or smells unpleasant, the potatoes will not be in good condition.