Select a pineapple with a firm, plump body without bruising or soft spots and green leaves at the crown. A green outer shell does not mean the pineapple is not ripe and contrary to popular belief, neither does the ease in which the leaves pull from the crown. Pineapples should be picked at their peak ripeness since unlike other fruits, they will not continue to ripen once picked. Whole or cut pineapple should be stored in the refrigerator.