Best JR option

Hi, we are planning a family trip to Japan in 2 weeks time. Here are our itinerary:
12/6 Narita to Shinjuku
13/6 Shinjuku station to Tokyo station. Shinkansen from Tokyo to Nagano. Nagano to Shinano-omachi *must arrive before 9am! (to Alpine)
14/6 Toyama to Shirakawago
15/6 Shirakawago to Osaka
16/6 Osaka to Nagoya
17/6 Osaka to Kyoto
18/6 Osaka USJ
19/6 Osaka to Hiroshima; Kurashiki
20/6 Osaka to Narita airport

Please advise what JR pass to purchase?
Are the abou te routes covered by the JR pass?
When is the latest I need to purchase the JR pass if I'm leaving my country on 11/6 night?
There 4 of us - 3 adults + 1 child