Confusion! Rail Pass and Itinerary

Hi, I have general confusion over whether our itinerary is going to work and which rail pass we should get and when to activate it? Should we get 2 week pass or activate one week pass at certain point?
17 October arrive Narita, staying in Shinjuku. General sightseeing and 2 return trips to Tokyo Stadium
21 October Shinjuku to Osaka
22 October Osaka to Kii-Tanabe
24 October Kii-Katsuura to Nara?
25 October Nara to Shinjuku
26 October Shinjuku to Yokohama return
27 October Shinjuku to Yokohama return
Possibly a trip to Hiroshima, back to Narita airport on 31st October to fly out on 1 November?
Personally I think the trip to Hiroshima is too far for 3 days...so may look at somewhere else.

Thanks,
Josie