There are so many railways and subways operating in Tokyo. They are safe and rarely late. However it's very difficult to know which route is the fastest or the cheapest. Even Japanease peopple don't know it. Beacuse the layout of those are complicated.
Many Japanese people use an application such as Japan Transit Planner to search the route. It's vaery convenient. You set the stations to get on and off and the click search. You can find the route to arraive in the shortest time.
Prepaied Rechargeable Card
There are two lins of prepaied rechargeable cards you can get in Tokyo. One is Suica. The other is Pasmo. If you get these cards and charge at stations you can get on trains immediately.
In addition the fee is normally a little cheaper than the ticket of a ticket-vending machine.
Suica
Suica was launched by JR East. You can get it at a multifunctional ticket-vending machine of JR East. The fee is minumum of 1000 JPY including 500 JPY of deposit paid.
Pasmo
Pasmo was launched by private railway companies and bus companies first. You can get it at a multifunctional ticket-vending machine of parivate railways.
If you get either one, you can use it for JR almost all private railways and buses in Tokyo now. In addition you can use even at convenience stores some shops and restaurants.