JR Pass for 10 days and Shinkansen question

Hey,

I gotta be in Japan for 10 days; the end of may til beginning of June.

Here's my itinerary:
day 1: Tokyo
day 2: Tokyo
day 3: Tokyo
day 4: Tokyo ~ Kanazawa
day 5: Kanazawa ~ Takayama ~ Nagoya
day 6: Nagoya
day 7: Nagoya ~ Kyoto ~ Osaka
day 8: Osaka
day 9: Osaka ~ Tokyo
day 10: Tokyo ~ Narita

What do you guys think? Should I consider buying a region-wise pass or a national wide?
And furthermore, if I were to travel by shinkansen, should I book the seat beforehand?
Or I just jump in with my pass? (I assume that my traveling time is rather low season as I checked from hyperdia...)

Thank you in advance!