Yamanote Line - Wikipedia, the free encyclopedia
Shinjuku and Shibuya are only a few minutes away from each other. If you know you are going to be taking the train every day for school, then you'll want to buy a monthly pass between the two stations.
This is one of the busiest lines in the world, really. It's the loop that goes around Tokyo. You don't need to worry about train schedules as the a new train comes every few minutes.
I don't know the rate, but it will be cheaper than buying a ticket (probably about 2 dollars) twice a day.