Tokyo to Kawaguchiko

Whic station has more bus leaving for Kawaguchiko - Tokyo or Shinjuku, timetable?
It it possbible to go by train from Tokyo station?

I think its pretty clear on the Japan-guide pages, more buses are from Tokyo Station:

http://www.japan-guide.com/e/e6905.html

As for train,

It is possible to go by train (you have to make connections and ride on regular local rapid trains), however as much as I love trains, taking the bus is simply much easier, much more comfortable, and costs about the same if not a little cheaper, plus no transfers or anything required as they are direct. I did it before going and coming back, and if I had to do it over I would take the bus.

I mistakenly took the wrong train from another station (can't remember which, but not Shinjuku) to Otsuki (Chuo line). It was the slower train and it stopped at every stopped. I then learned that the express train from Shinjuku to Otsuki only started in Shinjuku. I took that train on the way back and it was really fast, only a couple stops. I never took the bus there. But taking the train from Shinjuku (and making sure it's the right one with very few stops) was a good experience for me, and very fast. Only needed one transfer in Otsuki.

Looks like on this site that the train is about a half hour faster than the bus, but it's up to you which one you prefer. Either would probably be good. Bus leaves from Tokyo station. Train leaves from Shinjuku station.