Suggestions on JR Pass and Itinerary

Hello, I will be visiting Japan on 9th May -19th May 2024. 10N Trip covering Osaka, Kyoto and Tokyo cities. below is a broad starting itinerary I have put together.

Please recommend which is the best JR pass is applicable for us. (regional or all Japan) considering usage per itinerary.

Any suggestions to make the itinerary more efficient for us. We are a family of 3, myself, wife and daughter 11 years.

1) 9th May : Arrive at Osaka KIX airport 16:10pm -> transfer to Hotel near Shin-Osaka Station
2) 10th May : Osaka local sightseeing
3) 11th May : Universal Studios Japan (all day)
4) 12th May : Day Trip to Hiroshima and back to Osaka same day
5) 13th May : Osaka --> Kyoto, check-in to Hotel near Kyoto Station, local sightseeing
5) 14th May : Kyoto --> Nara day tour and back to Kyoto hotel
6) 15th May : Kyoto local sigt seeing (suggestions needed)
7) 16th May : Kyoto -> Alpine Route -> Tokyo (arrive same evening in Tokyo via Nagano)
8) 17th May : Tokyo --> local sightseeing
9) 18th May : Tokyo --> Mt Fuji Day tour
10) 19th May Tokyo --> check-out hotel, local sightseeing, depart from HND 22:55 back to home

Thanks a lot in Advance

Sunil Golani
India