Cheapest travel to Oda station

Hey,
I'm very unfamiliar with travelling around Japan. I'm looking for either
a) cheapest way possible
or
b) most comfortable way possible
between those two stations/areas:
Shimonoseki - Oda station
OR
Fukuoka - Oda station.

I hope someone can help me with this confusing request!
Any bus, train would be accepted. However, I travel with heavy luggage and wouldn't want to change transport more than once-twice.
Thank you!

What's the problem with the results given by Hyperdia?

Take the train. More comfort, not much of a price difference!

From Hakata station in Fukuoka:
Shinkansen to Shin-Yamaguchi.
Limited Express Super Oki to Odashi.
\ 10,490 reserved seat or \ 9,500 unreserved.
Only one transfer.
See Hyperdia for details.

Or highway bus from Nishitetsu Tenjin Bus Center to Izumo \8,440. Train to Odashi \580.

Thank you.
I'll figure it out once I can use the suggested website.. For some reason, it took me 3 hours to find info of the specific stations.