Tokyo to Mt Fuji and then Hakone?

Hi

I will be visiting Japan in early Sept.
What's the best way to get from Tokyo (Shinjuku) to 5th Station Mount Fuji? Then how do I get from there to Gora where my hotel is located?

Thanks

What's the best way to get from Tokyo (Shinjuku) to 5th Station Mount Fuji?

On weekends, with the direct bus. On weekdays, with buses via Kawaguchiko Station:
http://www.japan-guide.com/bus/fuji.html
http://www.japan-guide.com/e/e6905.html

Then how do I get from there to Gora where my hotel is located?

1) Fujikyu Bus from 5th Station to Kawaguchiko Station (about 1 hour)
2) Fujikyu Bus from Kawaguchiko Station to Gotemba Station (about 1 hour)
3) Odakyu Hakone Highway Bus from Gotemba Station to Hakone-Sengoku (about 30 minutes)
4) Hakone Tozan Bus from Sengoku to Gora Station (about 30 minutes)