On our trip throgh Japan, our route guided us from Kyoto to Tokyo. We chose the SHINKANSEN bullet train that took us from Kyoto station to Tokyo station in just under 2.5 hours.
Tickets are fairly easy to get and you can choose between a standard (2nd class – quite comfortable) and a green (1st class) car ticket.
For both, there is an option to make a seat reservation.
FYI: if you have extra large bags you will have to buy a special ticket.
Bonus tip: you can spot mount Fuji on the way from Kyoto to Tokyo