A) As soon as possible! Watch out for the "O-bon" holiday in mid August (it differs depending on the region, but I think it's from about the 14th-16th) as tickets are likely to be more expensive and planes/buses/trains are likely to be fully booked then. Also--as others have mentioned--keep an eye out for online deals.
B) As far as "best", that will depend on what type of person you are, but if you want cheap(er) options, then the nightbus--as someone recommended--would be one way to go. You could also just take a regular train/bus down if you have both the time and the interest (you get to see the scenery). If it's a train you would have to figure out how many times you would have to change trains and at which stations (but this adds to the adventure for some people).
Another option (which, I am assuming exists in Tokyo because I've never looked for them there), they DO have discounted bullet train tickets, but these are usually sold in vending machines/at vendors that are not necessarily all that close (close being a two to three minute walk) from the major stations, but chances are unless you have a local point them out to you, you will pass them by altogether.
If you have BOTH the money to spend AND will be travelling to MULTIPLE locations requiring long distance travel (Tokyo--Kyoto--Hiroshima--Sendai--Akita--Morioka--Aomori--Hirosaki, or hop over to other islands like Kyushu, Shikoku, or Hokkaido) then the Japan Rail Pass would be a good investment as it works for nearly all JR line trains and some JR buses (maybe ferries?) too. But, if you're just going to Kyoto, and you will be travelling around the Kansai area (plenty of cities and sites to see), it would be cheaper to use either the bus or regular JR train from Tokyo to Kyoto, and then once in Kyoto you can use the private rail lines to go to other destinations like Osaka, Kobe, Himeiji etc. and the fares are actually cheaper than JR.
Hope this helps and I hope your trip is AMAZING!!!!