How to get to Osaka from Kawaguchi?

I will be visiting Japan in few months to come.
From Shinjuku, I will be taking the bus to Kawaguchi sttn, where I am staying a night in one of the inn there.
Next day, I will be leaving for Osaka.
The problem is, I cant find any way of getting to Osaka from there. I am lost with the trains selections and station names.
Can someone help with this itinery? assuming I want the cheapest way of getting there.
Finally, I wanna stay a night in Kyoto after 2 nights in Osaka. As my other travel companions are not interested in going to Kyoto from Kawaguchi, I have to detour back to Kyoto after Osaka by ourselves. (me and Hubby)
Please advise what kind of train pass is good to travel to Kyoto and back to Osaka?
Thanks, I hope my itinery and questions are not confusing.

It is explained here:
http://www.japan-guide.com/e/e6905.html?aFROM=2157_6900

...on how long you want to take.

If you take the Shinkansen from Tokyo or Shinagawa station (reachable by Yamanote-sen from Shinjuku), it will take about 3 hours.

http://en.wikipedia.org/wiki/Tō;kaidō_Shinkansen

Or you can take an overnight bus from one of the main stations, like Shinjuku.

Either way, you will probably have to go back to a main station in Tokyo. I doubt that there are buses direct to Osaka from Kawaguchi.