Which rail pass to buy? 10 day trip

Hello,

I’m wondering what you’d recommend as the most cost effective travel pass for me and my partner?

Our plan is to fly into Osaka and leave from Tokyo. Rough itinerary below:

Osaka - stay for 5 days, with day trips to Kyoto, Nara, maybe Hiroshima.
Osaka - Tokyo bullet train.
Tokyo - stay for 5 days with a day trip Hakone, Mt Fuji

Would individual train tickets be better than a rail pass? And if rail pass is more cost effective, should we consider JR or just regional? We’d also like to buy a Tokyo rail pass if possible to cover our transport around the city for a couple days.

Thanks so much in advance, this is a huge help!