Im just heading there for 6days. Will be staying in Tokyo only. One of the day heading out to mt Fuji.
Suica or Pasmo is good enough. It’s like an Ezlink card. You can also use it in convenience stores and lockers.
As for Fuji Five Lakes, assuming you’re visiting Kawaguchiko and not 5th Station, you can take an expressway bus from Shinjuku Bus Terminal.