Trying to make the best decision

Hi Devin!

Looks like a great trip! Here are some thoughts:

1. I advise activating the Rail Pass on day 3, and purchasing the Keisei Skyliner + 2 day unimited metro pass at Narita to get you into Tokyo and give you free metro travel for days 2-3. This way you'll save the most as the return from Yamanouchi to Narita is expensive, and also get some discounted travel for the first few days you are in town.
2. For your trip you will need to take into account the following non-JRPass extra charges: The Keisei Skyline + Tokyo metro as mentioned above (though you can make good use of the JR Pass in Tokyo - here's a map of JR lines for reference). The train from Otsuki to Kawaguchiko - this is operated on non-JR Fujikyu tracks and costs ¥1100 each way. Kyoto and Hiroshima metro/trams are not operated by JR, and so you will need to either purchase tickets or a daily travel card.
3. You'll be able to get good use from a green car pass on the Narita Express, travel between Kyoto and Hiroshima and travel to Kawaguchiko. There are less green car equipped hikari running between Tokyo and Kyoto, so this is the main part of your trip where you may need to use standard class (or wait for a Hikari bullet train with Green car). The Green Car is very much down to budget I think :). Personally I am fine with standard class, but many people really enjoy the space and luxury the green car gives. The green car version of the JR Pass is exceptionally good value, and you can really get good value for money out of it.
4. I recommend travelling with a backpack. You'll find yourself travelling up and down escalators and will also find a backpack easier to store in the luggage lockers at the stations if you need to. As always, travelling light is the best approach! The luggage on the bullet trains are not checked, and either fit behind the last seats at the end of each passenger car, or fit in the overhead racks. If it is large luggage you should aim to store them behind the last seats in the carriage.
5. Here's a really good map that shows the direction of sunset/rise on the 1st of Jan 2013 (yellow line is sunrise, red line is sunset). If the weather is clear, I recommend being somewhere on the north side of the lake to Kawaguchiko to watch Mount Fuji backlit by the sunset/rise. In the link above I think Nagahama gives a good vantage point, but you'll be able to play with this more to find the best spot for you!

Hope this helps!