JR pass needed

Hi I am planning to be in Japan for 21 days
I would like to pick a pass that will allow me to go from Narita Airport to Osaka, Nara, Kyoto, Hiroshima, Tokyo, Mt fuji and then back to narita to catch my plane ? I have no ordered the pass yet My flight will be March 5th can I not pick up the pass at the airport If I order it today?. Also is the pass beneficial for my trip and if you could suggest best strategic way to move around the sites I want to visit along with the recommended pass. I would like to stay a few days in Tokyo to do shopping hence it is the last station I will be at.