Hi. I plan on vacationing in Japan for about 10 days. I plan on going to Tokyo first, then to Kyoto and then to Osaka (and maybe Nara).

1) What's the best way to get around each area? (Which lines?)

2) What's the best way to get from Tokyo to Kyoto?

3) What's the best way to get from Kyoto to Osaka?

From what I understand densha and shinkansen are the best options, so I was curious as to which lines you would recommend in order to make the most efficient use of my time there.

Any tips on saving time (and, IF possible, saving money too) would be greatly appreciated. Thanks!