Fastest route to cover Hakone - Kawaguchiko

I would like to go to these places.
Hakone-Gotemba-Lake Yamanaka-Kawaguchiko-Ikebukuro Tokyo.
Please advise the best route and transportation (bus/ train)that I should take to go to this areas. I will spend one night at Kawaguchiko and travel to Tokyo on the next day. Most important time saving to go from one place to another. And is it worth to buy Hakone Free pass or Hakone Fuji free Pass? Thanks.

Transport Tokyo to Hakone and Gotenba is well explained here:

http://www.japan-guide.com/e/e5206.html

Transport in Fuji Five Lakes area here:

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

Fastest way back to Ikebukuro would be taking the Highway Bus from Kawaguchiko to Shinjuku and change to JR Yamanote Line there

Thank you for your reply. FYI, I will travel from Nagoya to either Odawara or Mishima via bullet train. Will spend the day at Hokone then will travel to Gotenba. I've read there are Fujikyu buses travel to Kawaguchiko station which will pass through lake Yamanaka. I find that this route is nearer compare to if I choose to take the train which will cost me 4hrs ride. Appreciate if anyone could help me to tell me how to get to all the attraction place around Hakone. Then to travel from Hakone to Gotenba and from there to Kawaguchiko. I've learn that if drive via highway it only 60km and only took about 2hrs to reach kawaguchiko. I've have search/read around but could not find more details about the transportation.