Ares also seems to do well for public order, and gives three experience.
When I play Macedon, Ares goes in recruitment cities only and never when there is a resident governor. The "Bloodthirsty" trait is a -1 to Command, and -3 to Morale The Temple of Zeus has a Happiness bonus double that of Ares (50% vs 25%).

Would a farm temple really be helpful? The farms have some bearing with growth and plague, right?
Demeter is good for those "slow growers" that just can't seem to get enough population to reach maximum development. Once there, and stability is re-established (and possibly the addition of a governor with lots of influence), tear it down in favor of something better. Too much farm leads to high squalor

Against Egypt, however, how do you handle the chariots?
Persian Cavalry fronted by Cats. PC is not nearly as good as Cataphract Archers, but they get the job done. The Cats are there to keep the Chariot Archers from attempting melee, and then move in for the kill when the CA's are greatly reduced in numbers. Parthian foot archers are vanilla Middle Eastern archers. I only use them to defend walled cities where they are reasonably effective. You're right, I don't like slingers because of the direct line-of-fire, but they are effective, as you say, against chariots.