What kind of rail pass do I need?

Hi. On october 6 I am travelling to Japan for the first time. I have the following initiary:

Oct7 - Arrive KIX - Spend 3 nights in Kyoto.
Oct10- Hiroshima - Spend the night on Miyajima
Oct11- Nara
Oct12- Koyasan
Oct13- Tokyo
Oct19- Depart from Tokyo Narita airport.

So my question is: What kind of Rail pass would you recommend?

The initiary is kind of carved in stone as we already have booked and payed for most of the hotels. But any tips for our travel would be highly appreciated.

Thanks.

The 7 day pass will pay off on your itinerary. I would activate it on the day you arrive at KIX on the 7th, and use it to take the express from the airport into Kyoto.

The last day the pass is valid is the 13th, where you will use it to get to Tokyo on the bullet train.

Once in Tokyo, I'd either buy single tickets or get a Suica card to travel around. Get to the airport using a Keisei express rather than the expensive NEX limited express.

As a side note, I would use the Nankai private line from Osaka to get to Koyasan (using the JR pass involves a lot of random connections). They offer a Koyasan World Heritage ticket that gets you to Koyasan, including the cablecar and bus, and also some discounts at the temples.

http://www.japan-guide.com/e/e2358_012.html