Taking Shinkansen on the way to Kyoto from Tokyo

My boyfriend and I are going to Japan next month, Tokyo first. But, we want to see other places there and we were advised to take Shinkansen on the way to Kyoto and other towns from Tokyo. It seems their train system is much more developed than in other countries. Can you tell me something about it?

Tokyo, Nagoya, Osaka and Kyoto are all connected by
Tokaido Shinkansen, first started back in 1964 (speed
of those trains was around 200 km/h, now it is over
300). There are three categories of the trains: Nozomi
(the fastest, stops only at important stations),
Hikari (a bit slower with more stops) and Kodama
(slowest, stops at each station).