Need help knowing which pass to buy

I am traveling to Japan from March 14-23. I arrive and depart from Osaka but plan to go to Tokyo from March 19-22. Should I buy a 7 day pass and activate it on March 17 so I can use the Shinkansen line both ways? Or do I have to pick the JR pass up at the airport upon arrival which would mean the the 7 days would expire before I use the bullet train to get back to Osaka. The 14 day pass is a lot more expensive than I think I need. Please advise about which pass I should get. Thank you so much.