It depends on what is definited as"best".
I think "best" should be all-round,including high availability,great stat,mobility and adaption to different battle situations(for example ap).
So I favor(red for late,blue for early)
heavy cavalry:
Lancers(avoid combat with ap) and
Sicilio-Norman Knights(exclude Athanatoi as BG)
light cav:
hussars(a bit earlier than Stradiots) and
Hohuchi(good all-round )
horse archer:
Mamluk archers(ap) and
Bekh Druzhina(6 attack)
archer:
Pesante Archers(so early as a late unit with 6 armor) and
Mourtatoi(it has stakes and is so popular)
infantry:
Royal Guard(the strongest ap infantry) and
Croat Axeman(strange,but 7 ap is too strong to be ignored,also cheap,light and easy to get)
special:
Naffatun and
Constable of Jerusalem