Ji Chang wook or  Kim Mu Yeol or Lee Soo Hyuk 

Ji Chang Wook (Gogukcheon) most likely. He plays an honorable and competent king whose death in history is the catalyst. They also seem to depict him as the male lead.

Lee Soo Hyuk (Balgi)  is definitely the antagonist. He is the most logical successor of Gogukcheon but Woo will be against this and support Sansang.

Kim Mu Yeol (Prime Minister Eulpaso) will likely next to Woo have the most screentime when the succession crisis breaks out. Definitely very important.

Kang Young Seok who plays Sansang would in general have been the logical choice if you go by history. However despite being a key character he is just in the support cast.