There are three ways to come to Seki from Nagoya.
1 You can go to Seki directly in the express bus from Meitetsu bus center(about 80 minutes )
total fare 1030yen
2 You can use JR line or Meitetsu line from Nagoya to Gifu(about 20~30 minutes)(470 yen)
From Gifu to Seki, Gifu bus is available.(about 60 minutes) (680yen)
total fare 1150yen
3 You can take Meitetsu line to go to Shin-Unuma(about 30 minutes) (600 yen)then walk to JR Unuma station to go to Mino Ota. (about 10 minutes) (210 yen)At Mino Ota station you take Nagaragawa Tetsudo line to go to Seki.(about 20 minutes). (460yen)
total fare 1270yen
As I am sure you can see, the fastest way is using bus.
If you would like to enjoy riding trains. I recommend choosing number 3 , but you have to wait for a long time to catch Nagaragawa tetsudo train to go to Seki. In this case you can enjoy walking around Minokamo city.