[1 Authority +1 Influence invested until Heliocentrism debate finishes. Takes 1d10=10 turns.] [1/10]
Damnit.
I thought light v heavy was a function of the armor, rather than the arms?
I'll clarify the option.
Heavy v. Light is a dichotomy that didn't really exist historically. Everyone wanted to wear armour, it's just that it was so expensive (due to low levels of iron production), that not everyone could get some. Both Light and Heavy infantry tended towards using the same weapons (polearms) since they gave you range (safety) and additional striking power. When dealing with someone in heavy armour, you couldn't really penetrate it with anything less than a couched lance from a charging knight or at very short range from a powerful steel windlass crossbow or early firearm. You could, however, wound the man underneath the armour; repeated strikes to the body can fatigue them, bruise them, or even concuss them, rendering them helpless so they can be dispatched with a stab between metal plates. It's why striking the head and using polearms was so ubiquitous.
The 'types' of troops historically would be: heavy cavalry, infantry, missile (archers/crossbows/guns), and skirmishers. Skirmishers were basically entirely supplanted by light cavalry within the Medieval period; a horse can simply run faster than a human and societies had become wealthy enough to be able to afford to support them. It was only a few really marginalized groups or ones where the terrain did not permit it that maintained a tradition of skirmishers as a distinct type of light infantry. Horse archers were the king of skirmishers.
Infantry generally were as heavily armoured as they could afford. This usually meant a metal helmet of some type and a linen coat with either lamellar or maille over top of it if that was within budget. Note: even the linen coat on its own was extremely effective. It was very difficult to pierce or cut through and provided enough protection against arrows that they wouldn't kill you, even if they wounded you enough to get you out of the fight. Heavy and blunt weapons were very popular since even if it could defeat the armour, it could break bones underneath it, incapacitating the enemy. It was only with the adoption of widespread lamellar or plate that armour truly became proof against hand weapons and started to require real polearms, whether that was in the form of billhooks, halberds, poleaxes, pole hammers, etc.
Heavy cavalry developed its distinct role because of their ability to break infantry formations, mostly through fear. Generally, if infantry held firm, heavy cavalry would get bogged down and eventually cut down. This was, of course, a big ask from infantry since it'd be like standing up in front of a speeding tank based on your commander's say so.
Missile troops weren't super effective since armour was more than adequate to protect against all but freak shots when at range; even padded linen gambesons. What they were good at was sapping morale and baiting the enemy into breaking formation. It's hard to sit there under a hail of arrows, slowly being injured or killed by random shots.
Lastly,
@Aranfan you mentioned that our Levies used mail, but I don't think that's realistic. Making a mail hauberk requires about 750 man-hours for butted mail and 1,000 hours for riveted mail. To turn out a set of munitions plate requires 20-30 hours. Munitions plate basically consists of a breastplate, skirt, shoulder guards, and a helmet of some description. It's one-size-fits-all so it's made en-mass for the general soldier with only a few touch up generally required for final fitting. Simple plate armour is so much faster and cheaper to make that it's not even a comparison. Once Europe discovered enough about metallurgy to move towards plate, they never looked back and mail was obsolete. The problem was the general Guild system and the small size of different states; they jealously hoarded the secret to make metal plate so it took forever. For us, however, with the Guild Industry, we produce enough metal and have sufficient know how that switching to munitions plate should have been accomplished long ago. Mail is astoundingly more expensive, harder to maintain (mail is badly affected by rust), and much less effective (especially for butted mail). Munitions plate first started to proliferate in the 1400s and became ubiquitous across the 1500s so it isn't a profoundly out-of-place technology for a place with enough of an industrial base that we compare favourably to the 19th century.