It's kinda hard to think of names when we don't know the tech-tree and/or any hierarchy, sure we can guess but the information is lacking. That aside a few generic ideas.

Japan:
Minor Dojo -> Famous Dojo -> Imperial Instructor ...for regular sword infantry
Weapons Cache -> Provincal Armory -> Sohei Compound ...other infantry
Horse Trainer -> Calvery Stables -> Imperial Stables
Local Police -> Provincial Police -> Shinsengumi Office
...maybe get elite samurai from Shinsengumi...
Chinese techniques -> Legendary Rice -> Irrigation

China:
incorporate regular infantry into city expansion
Minor City -> Walled City -> Stronghold -> Banner Stronghold
Minister's Household -> Imperial Household -> Imperial Palace ...for elite troops
Courier Station -> Army Stables -> Imperial Armoury ..for calvery & specials

Demon:
Haunted Battleground -> Ritual Alter -> Necromancer ...for undead infantry
Deep Chasm -> Shadowed Lands -> Planer Rift ...for demon infantry
...just an idea but maybe you can have demons and undead be mutually exclusive...
Bandit Hideout -> Derilict Stables -> House of Nightmares ...for calvery