Yamanashi-Hakone itinerary advice

Hello ,
we are a couple going to Japan for the first time for our honeymoon.
we will be first staying in Tokyo for 4 nights then we are going to Hoshinoya Fuji which is in Yamanashi for just one night and then we wanted to go to Hakone the next day. From what I found online, it's only 45 minutes drive but somehow it was also saying 4hours bus ride, is that even possible that there s no faster way ? we re only staying one night in Hakone and then we are going to Kyoto.
I have no idea how long all these travels will be and how easy or difficult it is to take trains and buses in Japan. I have to admit I am as nervous as I am excited !
If anyone can help us with itinerary or advices on transportation we would very much appreciate it !
Thank you all
Morgane & Ian

public transportation in Japan is generally easy to use, efficient, almost always on time to the minute, and can get you almost anywhere you want to go (expect some walking). The large major train stations can be intimidating, especially during peak times trying to navigate your way through waves of people. But there are information booths and people who will help you get to the right track etc. Keep in mind that there are many different rail companies. For example, in Tokyo there are JR trains and the Tokyo Metro subway.
Hyperdia is a great site to help you plan train travel but you've got to know the exact spelling of the stations. You can also use google maps to help you.
in terms of travel time, from Tokyo to Kawaguchiko by train is about 2 1/2-3 hours. From Kawaguchiko, you could catch the bus to Gotemba and from Gotemba to Hakone (I've never done this but it seems doable and it would take about 2 1/2 hours or so). From hakone to Kyoto would take about 2 1/2 hours by train. Anyway, hope you enjoy your honeymoon in Japan!
p.s. travel light--don't take large suitcases unless you plan to use luggage forwarding services. Navigating the stations and public transportation with too much luggage will be miserable!