I'm sure there are many topics about the rail pass already, but yeah, your situation is pretty much what the rail pass is made for. You really need to be going at least a couple of long distance legs (or a *lot* of short distance legs) for the rail pass to make sense, but it certainly would if you plan to travel the entire length of Japan.

I'm not sure if there's any difference in using the rail pass nationwide - I've only used it on JR Central and JR West. I'd guess it's just as easy to use everywhere, though.

I've only gotten a rail pass once (I usually stay around Tokyo or Osaka, which makes it not worth it) and I got a green car pass that time. I never regretted that at all, although it can depend on what kind of traveler you are. I appreciate the quiet and extra seat width and legroom in the green cars, plus it's a bit easier to deal with luggage (the luggage space is usually empty, because the cars are less full). Also they come through with the snack carts more often in the green cars. But there is certainly enough space for most people in the ordinary cars, and they're usually not mausoleum-quiet like the green cars are either, so if you're in a group, ordinary might be better.

One thing to consider now is that on the newer trains, the green cars have power at every seat for your electronics, whereas the ordinary cars don't. But it's still kind of a crap shoot if you'll get one of the newer trains.