Here is a link to help you think about purchasing your Shinkansen ticket.

A tip from a past intern:

If you buy Shinkansen tickets at a machine or ticket window, you can use the same ticket to transfer onto JR lines without paying extra: https://shinkansen.tabiris.com/shinaieki.html. For example, at Shinagawa, you could go straight through the JR transfer gate from the Shinkansen platforms to the Yamanote Line 在来線 platforms and travel within the Tokyo City limits for the same fare of the Shinkansen ticket. It could save you some time and money.