Which pass is best? Tokyo>Kyoto>Hiroshima>Fuji>Tokyo

Hi there. We are a party of 4 adults and in Japan for 2 weeks arriving 24 October. Our itinerary is:

Haneda Airport - Tokyo 4 nights
Kyoto 5 nights (and planning day trips to Osaka and Nara)
Hiroshima / Miyajima - 1 night
Mt Fuji / Kawaguchiko - 2 nights
Tokyo - 1 night - Haneda Airport

We'd like to travel by train as much as possible so is the best option a general/national Japan Rail Pass, or could we get better value with a Regional Pass that covers most of what we are looking to do?

Many thanks!
Graham