I had 12 trips to Japan on business and the train is the best way to get to the city from Narita.
When you're traveling about, it's ok to have 10 or 15 minutes between trains if you have to make connections - They are ALWAYS on time, no need to allow an hour like you do here.
The express trains and Shinkansen have a trolley service for drinks and snacks, the girl won't speak english, but poining to what you want works fine. Make sure you try the selection of sandwiches and the dry fish too.
For a day trip out of Tokyo, take the JR past Yokohama to Kamakura, where there are seveal temples and things, including the famous Giant Buddah
http://www.kamakuratoday.com/e/sightseeing/daibutsu.html
http://www.japan-guide.com and http://www.sunnypages.jp are useful too
Remember that many restaurants will require you to take off your shoes, so pack some new socks, you don't want to be embarassed by your toes poking out.
For food, try shabu-shabu and tempura. If on a tight budget, the Yoshinoya franchise is the local equivalent of McD and has pictures for you to point at. Lots of restaurants have plastic replicas of the meal in the window, so you can point at those too.
Have a great time and worry about the credit card bills when you get home