Hi Cardinal.
When I first started playing I hated priests! The damn things were always converting my units...I never played them because they were too tricky.
As I have played more I have learned the value of priests, especially in healing (Medicine is a steal at 150 gold!) and later in the game when resources become more scarce. The following example serves the purpose of demonstrating how a priest can quickly change the course of a battle.
Assume opponent's 6 elephants are attacking your 2 elephants. With 2 priests you can convert two of the elephants and then it's an even battle.
(I know, who doesn't attack with mixed Units, but it's just an example!)
Now you won't have much luck with priests against a Civ like Assy, which is going to play with lots of CAs and HAs, two units very tough on priests. Similarly, against the seemingly ubiquitous Scythes, Priests are worthless (Except if behind walls, of course). But if you see any of the following Units priests are simply the perfect foil:
Elephants (well, duh.)
Elephant Archers
Academy Units
Catapults
All towers but Ballistics towers
Triremes (stand out of their range)
Priests not only convert troops, they can have a defintite psychological effect on your opponent, who will be quite disconcerted when you "steal" their units. It will, often times, put them on the defensive in a fairly even game.
Speed 1.0 is best for priests, because they do require scads of micromanagement. But if you put in the time (and practice) they are very rewarding. And useful, as long as you use them when appropriate (see above). Incidentally, for both Phoenecian and Egyptian, the Priest/Scythe combo is a very nice one indeed. There are some counters, but not many. Scythes, en masse, can tear up most everything thing but Academy and Elephant units, which are both easily convertable. (Excepting walls).
So, I would suggest playing a Civ that gets all of the priest upgrades and also can get the Scythe upgrade and working at this combo to begin your practicing with priests.
-- Prince Bolkonsky