My personal desire is not quite RPS.

I want sword to be offensive infantry and spear to be defensive infantry. I want spear to repel charges and die very slowly. I want their job to be to hold other units, not kill them. "Sword" (By which I mean all heavy shock infantry) I want to be bowled over by charges, but on the offense, to be killing machines.

I want light cav to be great flankers and pursuers but terrible at frontal charges. I want heavy cav to be able to dash heavy infantry to pieces with a charge, but take horrible losses and be held for a long time charging a spear unit head on. I want them to be able to beat, barely, a spear unit of equivalent period in a frontal attack (The idea is to make it monetarily impractical) but lose to pikes every time.

I want archers to annihilate anything if they manage to achieve flanking fire. I want them to generally reduce most units badly when firing frontally as well. Missile troop balance is simple, at range, they win. In close, they die.

That's what I want.