Found this one. Fields of Glory II. It seems this has an Imperium and an Medieval editions. I have the first. It's about the battles and campaigns of the antiquity and early medieval times. Greeks, Romans, Persians, Germanics, Huns, Arabs, Vikings, I think Babylonians too perhaps. And some. Has a handful of DLCs that added more content.
It's a turn based tactics game, adapted from a tabletop boardgame, so the rules are tested by time. It has a great variety of units and all should conform to historical time and place. I played only 2 tutorial battles (successful) and started the Roman campaign against their early neighbours, Etruscans, Samnis, etc. Got my ass handed to me. Although I did not gave the thought it deserved, and I'm not familiar with all the rules. For example before each battle the user gets X points he can buy units with. I dunno if the remaining points are transferable to the next battle of the campaign, or one should spend it all (I did not do that, so I was in numerical disadvantage, like 24K vs 14K or something).
Additional information: the map is square based not hex, probably better for simulating phalanxes meeting with each other and forming lines and such.
The graphics are fine for me.
I give a very good rating for this. Like 8 pilum out of 10. It perhaps 10/10 perhaps 6/10, but I have not played enough.