There are 20 playable characters. You start with 3 and the other 17 can be unlocked in Story mode (first option in the menu). You should get a minimum of B grade at the end of the missions to unlock a character.

Character	How to unlock
Ba Jio	Clear mission 8 with B grade.
Duke Hyou	Clear mission 6 with B grade.
Ei Sei	Clear mission 9 with B grade.
Hou Ken	Clear mission 9 with B grade (Hard mode).
Jo Kan	Clear mission 1 with B grade (Hard mode).
Ka Ryo Ten	Clear mission 7 with B grade.
Ma Ki	Clear mission 6 with B grade (Hard mode).
Man Goku	Clear mission 8 with B grade (Hard mode).
Mou Bu	Clear mission 10 with B grade (Hard mode).
Muta	Clear mission 2 with B grade (Hard mode).
Rankai	Clear mission 4 with B grade (Hard mode).
Sa Ji	Clear mission 3 with B grade (Hard mode).
Shou Mou	Clear mission 7 with B grade (Hard mode).
Shu Ki	Clear mission 5 with B grade (Hard mode).
Shunmen	Clear mission 4 with B grade.
Tajifu	Clear mission 5 with B grade.
Tou	Clear mission 10 with B grade.