Well I've only played seriously with Casse, a tiny bit of Makedon(in 1.0), and Saba (in 1.1) so I have little or no experience with cavalry, but here's what I have

Missile: Arab Slingers/Archer-Spearmen - They proved essential to conquer arab rebel towns. Specifically to take out those pesky Sabean nobles, before my infantry rush in.

Light Infantry- Red Sea Light Infantry(Technically H. Inf on the battlefield )- What's not to love about guys with battleaxes charging into a load of missile units (or any units for that matter)

Heavy Infantry- Milnaht. Couldn't have taken Germany without these guys. A very good all-round unit.

Cavalry- Makedon Strategos - Won a lot of tight battles with these.