One of the things that makes this confusing is it isn't just period improvements. The game follows age of empires, where you are basically starting your civilization from scratch, and it has the same feel. So militia aren't just supposed to be early infantry, they're also supposed to be whatever cheap men your tiny kingdom can muster. The term militia sort of implies less trained or inferior levies.
The men at arms are your first quality soldiers. This term was used in all ages to describe fighting men. So for feudal age it would make sense to be chain mail. The Long swordsman isn't really a good name for an upgrade, and Two handed swordsman upgrade is nonsensical, as two handed weapons existed along side bastard and one handed swords. The champion is in the same age as the two handed swordsman and he again speaks of a quality upgrade, not a period upgrade. Champions are just the best swordsman.
And that's the best line. Cavalier and knight mean the same thing, archers and crossbowmen are different weapons entirely, as are pikes and halberds. They don't work as period OR quality upgrades.
If i was doing this, I would go like this:
1. Militia - Cheap looking unit. Leather/chain mail
2. Man at arms - Quality chain mail, typical early norman or crusader look
3. LSM - Mix of plate and chain mail to imply some transition
4. 2HSM - Plate mail suit
5. Same as above, but with feathers, a cape, or something like that to show he is a champion.
Your pictures are pretty good, but I'd make the norman the man at arms and make the militia a cheap looking unit.
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