Very well put, I have very little to add about trains.
The one thing I'd like to mention though, in Osaka area there are ICOCA cards, and I think in Tokyo area it's Suica? And they can make your life a lot easier, basically cash cards just for the train and you can get the deposit back once you leave. I give one of those to any friend or family that visits so they don't have to worry about buying tickets or knowing how much it costs to go someplace.
They are a little tricky to get at first (at most major stations you can get them talking with staff in a room next to the gate), but if you'll be taking the train often it's worth it imo.
JTG: Smart Traveling Japan - SUICA and ICOCA :: YokosoNews - Japanese Culture, Lifestyle and Entertainment
there are probably better sites for it, that's just a quick google ><