Tokyo's train system is complex: 30 companies run 121 train lines that connect 882 train stations. Between any two stations there are numerous possible paths: each with different prices and schedules. Adding to the confusion: there are local trains, express trains, rapid trains and special rapid trains. Guessing the best path by looking at a map doesn't work.
These days everyone uses route finder websites from their mobile phone. These services are free. They can sort routes by price or travel time. Two such services (in English) are:
Jorudan Train Route Finder
These services can also tell your the time of your first and last train. It's important to remember that train lines aren't 24 hours in Tokyo.