I think Spartans are the best overall infantry unit. People like to make comparisons to Urbans by saying they beat Spartans in 1 on 1 battles, but that doesn't prove overall effectiveness with multiple units in battle, and that's where it really counts. Skilled players can defeat Urbans with Spartans, and they do. Besides, Urbans are very nearly a fantasy unit. Yes there were some, but very few, and as far as I know, they were responsible for absolutely no major victories in real life combat. The Spartans were the real thing.

I hate to admit it, but probably the best overall cavalry unit is the stinkpot Desert Cavalry. They beat Praetorians and Companions, and even Cataphracts in actual battles. They aren't flashy or expensive, but they absolutely kill all other horse units except Head Hunting Maidens, which give them a close run. They aren't suited for attacking formed infantry, but they deal very well with other cavalry. That being said, I hate that they derive their advantages from inflated unit size and armor piercing weapons. And I hate the Egyptians, too!

I think Pharoah's Bowmen are the best archers. They have better melee stats than the middle or even top tiered infantry of many civs. They have excellent range, good morale, and are just generally very obnoxious. I hate the Egyptians! Foresters are okay, but Gaul rarely survives long enough to actually field them.