Do we need a jp railpass?

We arrive at narita and then travel to Tokio
4 days later we travel to Mount Fuji
Next day to Matsumoto stay 2 night
From matsumoto to takayama
From takayam to kanazawa stap 2 night
From kanazawa to Kyoto

Wich railpass souls you advice us? The Japan Rail Pas or one of the regional passes
We Will travel around the city as wel to explore or do Jokes

Thanks for your replay
Elke from Holland