Commercially grown bananas are picked green. They mature once picked, so there is no benefit to choosing ripe fruit except if the bananas are to be eaten soon after purchasing.
Do not store bananas in the refrigerator as the skin will blacken and become spotty. If you wish to speed up the ripening process place bananas in a brown paper bag with a ripe banana or apple. Bananas can be frozen whole or in pieces.
They are available all year with the greatest supply in Summer and Autumn.