To Buy: 
Select unwashed potatoes that are firm and dry. Avoid any with green patches - the green is an indication of the toxin solanine. Avoid also potatoes that are wrinkled and spongy. 
To Store: 
Old potatoes will keep for weeks in a paper bag with plenty of ventilation. 
Never store potatoes in plastic bags. 
New potatoes should be used within a few days.   
Tips & Tricks: 
For lower GI buy waxy potatoes.  
Cooking Tips: 
Floury potatoes (Bison, Sebago) are suitable for mashing and baking (and chips, although no-one reading this site will be making chips!) 
Waxy potatoes (Desiree, Kipler, Pontiac) hold their shape and are suitable for boiling and salads.