Best option for Touring Japan

Hi We are a couple and plan to tour Japan We wish to leave Tokyo for Lake Yamanakako. The following day we would like to visit Oshini Hakkai . and then travel on to Takayama.
The next day we want to go to Gokayama and back to Takayama . The following we would then go to Kanazawa. The following day travel onto Kyoto for two days. We are thinking of going to Nara after that or Hiroshima. We are allowing two days in Nara ( or Hiroshima ) before travelling to Nagoya where we will stay two days before returning to Tokyo. It will be eleven days all up from when we leave Tokyo until we return.
I am confused as to the best transport to take for our tour and the cheapest option. Heopfully we can get some advise on this.