I was in Japan at Easter this year for 9 days and had used a 7 day JR National Pass to travel from Tokyo to Kyoto, then Kyoto to Hiroshima and then back to Tokyo.
I purchased the standard pass rather than the Green Car pass. The Green Card pass is only really worth it if you are travelling in peak holiday seasons as the normal class cars will fill up quickly. The cost of a return ticket between Tokyo and Kyoto is roughly around the same price as standard JR pass so offers excellent value for money plus you can use it on any of the JR rail lines and also the Miyajima ferry. You cannot use the JR Pass on the NOZOMI” and “MIZUHO" Shinkansen. The difference between these two and the other Shinkansen is that they stop at fewer stations. For example I think the time difference on them between Tokyo and Kyoto was about 15 mins.
Depending on when you actually plan to use your JR pass will determine when you need to activate it. When you activate the JR pass they will ask you what date you want it to start. The time period will then start from that date. So if you know you're going to be visiting Osaka/Nara towards the end of your stay, activate so it the final day expires at the end of your holiday. This way you won't be having to fork out for tickets because it has expired because the start date was the date you arrived in Japan.
I am planning to go back to Japan in September next year for about 11/12 days and will only be buying a 7 day pass because I am planning to do my travelling around the end of my trip.
Hope this has helped and any other questions please let me know.
And enjoy beautiful Japan!