Which route to Takayama and Shirakawago

I could take Hokuriku Shinkansen to Toyama and then travel to Shirakawago, follow by Takayama.
I could also take JR train from Tokyo to Nagoya, to Takayama to Shirakawago.
Please advise the pro and cons, eg time spend on traveling, scenic train ride and etc. Thanks. Jin

In winter, the weather on the Pacific Ocean side would be better. Mt Fuji with snow on top would be seen. The Japan sea side would be mostly covered by snow. Hokuriku Shinkansen is brand-new, so would be the seats and others. What would be the next of Shirakawa-go and Takayama. I am more interested in Tokyo-Toyama-Takayama-Shirakawa-Kanazawa-Kyoto chain.

Use Hyperdia http://www.hyperdia.com/en/

Depends on what time you depart from Tokyo

Could be Tokyo - Toyama - Takayama
or
could be Tokyo - Nagoya - Takayama

For Takayma - Shirakawago - Takayama your could use Nohi bus
http://www.nouhibus.co.jp/english/shirakawago_kanazawa.html

or join a tour
http://tour.j-hoppers.com/shirakawago-tour/

Hope this helps!!
Have Fun!!