I love Shinkansen!!! We need it in the States. Really comfortable (the seats are spaced so far apart I could fully stretch my legs!!) You only have to show up a couple minutes before your train (not like hours for planes) and no security pat downs!! And you always have a view since you aren't stuck in the clouds!
There are several shinkansen services to Kyoto: Nozomi (fastest), Hikari (middle fastest), and Kodama (slowest b/c it is essentially a "local train" and stops at every station).
I took the Kodama train since it was the cheapest!
It was really nice seeing rice paddies and tea bushes, especially after being stuck in Tokyo for a few months.