Japan is great year round, so first check your availability. I am going next month.
If availability is not an issue, then Dec-Jan if you like winter and snow, Feb-April if you like spring, skip first week of May and Aug-Oct for the fall colors.
Japan is vast and there is literally so much to explore and see that even 1 month is not enough. I am going for 16 days.
In 1 week, I think you might only be able to hit Tokyo-Osaka-Kyoto at the surface level because of travel being involved. You won't have time for regional areas.
I would recommend to restrict yourself to Tokyo and Osaka only.
As for the rail pass, depends on you. 1 Shinkansen ticket generally costs around 4-5k, assuming you take 2 of these and rest as local commute, the pass won't be worth it.