Advice for New Years travel and hatsuhinode

Hello.
I was planning on being around Japan around the New Years time and I wanted a bit of help with my plans around then. I understand that New Years is one of Japan's biggest holidays so I'm not quite sure if I'll need to accommodate for that in my trip.

The main highlight is, of course, participating in typical New Years day activities. In particular, I really want to see the first sunrise of the year over Mt. Fuji. I was looking to go to somewhere in Yamanshi to do this. What are the recommended spots to view the sunrise from? I'd like to stay somewhere close by so I don't have to travel far on New Years eve.

Another question is getting to and leaving Yamanashi. I plan on leaving Tokyo fairly late in the afternoon on 12/30 (around 6pm or so). Would there be any trouble getting to my hotel in Yamanashi? And I'll also be leaving to Osaka early 1/2. Any troubles there? I realize that this greatly depends on where exactly in Yamanashi I'll be staying but I've read things like needing to reserve train seats around New Years, so I'm already pretty worried.

Thanks for all the help.