Hi there,
Green Class is by reservation only This means you have to book the tickets beforehand. This can be done up to 5 minutes before departure (although I'd suggest taking a bit more time).
You can however use a non reserved ordinary seat without reservation, if you are really in a hurry.
I don't have a full list with lines not included, however you can use other awesome interactive map to see all lines covered and Plan with Hyperdia to only use JR lines.
I can also let you know what is covered and what not if you tell me your travel plans.
Hope this helps,
Daniel