Which is rail pass is best?

Hi there,

Little overwhelming with all the options and calculator so thought id see which you thought would be the best for my itinerary which is as per below.

1st-6th Oct Tokyo
6th-9th Kyoto
9th-10th Hiroshima
10th-14th Osaka

We were also hoping to do a day trip to Hakone whilst we are in Tokyo and a take the ferry to Miyajima and day trip to Nara from Osaka.

Can i confirm the pass will only begin from the day you activate it? I am thinking i may be able to do the 7 day pass if i start it the day i leave from Tokyo. Im hoping i worked it out correctly.

Thanks
Veronica