Shinkansen's are going to cost you some cash, unless you get an unreserved seat - that'll be cheaper, but be prepared to move if you're in someone's seat. I took local trains, and while it was longer, wasn't bad at all especially if you are traveling with someone. The cost is SIGNIFICANTLY cheaper.
+1 on the not going during New Years - you can go, but everything really does shut down during that time, especially ATM's for foreign cards. I got stuck in Hiroshima during that time, and if it wasn't for a SUPER understanding hostel, I wouldn't have had any cash (they charged me extra for the room, and gave me cash back).