14 days or 21 days pass

Hi All
Hope yo can assist me. My wife and I are visiting Japan in October. Our route is as follows

Land haneda airport early October
Stay Tokyo 4 nights (visit to Mount Fuji )

Travel by train to Kyoto for 4 nights ( trip to Nara)

Travel to Hiroshima. 2 nights ( trip to Miyajima )

Travel to Osaka 4 nights ( trip to Kobe )

Travel to Haneda 1 night

Works out at 16 nights. Will probably do lots of travel on underground and railways at each stop.

My questions are
is it worth getting a14 day jpr pass or 21 days.
And is the first class ticket worth getting rather than the standard.
Does the jpr cover the underground and all the buses in the stated stops.
How early can I book the pass.

My apologies if the answers are here on the forum already but wanted to make sure I understand it all correctly

Kind regards
Treds