For a 7 day pass to be worthwhile, you need to spend over ¥28,300 on tickets. For a 14 day pass to be worthwhile, you need to spend over ¥45,100 on tickets. Lets take a look at your itinerary:
- Tokyo > Otsuki: ¥3060, (86mins, 87km)
- Otsuki > Osaka: ¥16000, (279mins, 604km)
- Osaka > Nara: ¥780, (59mins, 48km)
- Nara > Osaka: ¥780, (55mins, 48km)
- Osaka > Kyoto: ¥540, (29mins, 42km)
- Kyoto > Osaka: ¥540, (28mins, 42km)
- Osaka > Hiroshima: ¥10150, (104mins, 345km)
- Hiroshima > Osaka: ¥10820, (109mins, 345km)
- Osaka > Tokyo: ¥13950, (194mins, 556km)
- Tokyo > Narita airport terminal 1: ¥3140, (58mins, 79km)
TOTAL: ¥59760 for 10 legs
As you can see from your ticket costs I can recommend both lengths of Rail Pass to you. a 14 day pass will save you ¥14660, and a 7 day will save you potentially ¥31,460. You will save more if you elect for a 7 day rail pass, however you will have to compress your trip to make sure all the long distance leg to Osaka fits within a 7 day period.
You can use the JR Pass for travel in Tokyo on JR lines although you will probably also supplement this with Metro travel. Here is a map of JR lines within Tokyo for you to refer to. You can also use JR lines in and around Osaka - here is a map with JR and other lines in Osaka.
The choice of a regular or first class seat is a tough one! Here is a blog post on the benefits of the green car. Certainly it will be quieter during Golden week than standard class tickets.
Hope this helps!