Narita-Kyoto-Osaka-Mt.Fuji-Tokyo

Hi,

My girlfriend and I are going to japan April 10-14,landing in Narita at 4pm on the 10th. My plan is to go to Kyoto that night, stay and travel around Kyoto/Osaka until April 12. Then we want to go to Mount Fuji from Osaka on the 12 (leaving Osaka in the early afternoon). The thing is I couldn't decide whether to do Osaka-kawaguchi-hakone or Osaka-hakone-kawaguchi. Which one would work better?? In the way that I will be able to explore more in Mount Fuji. Should I take the train from Osaka to Tokyo or shinjuku??? ....We're leaving Mount Fuji early morning to go back to toyko and then to narita airport.

Thank you!