Under each slot, I have listed the item enhancements generally in order from the best enhancement to least best. For most slots, I have a couple of options and ranked them this way, so that if you do not want to spend all the mats on the best enchantment (i.e. on a non-epic item that you will hopefully replace soon, etc), you can find a cheaper alternative that is still good. If you're still in greens and don't want to spend money on expensive enchants, at least pick up some Heavy Borean Armor Kits for the applicable unenchanted slots.
Some points to consider about my rankings:
In general, these suggestions apply for both Holy AND Discipline specced PvE healers. The only caveat to that is that Discipline priests are more likely to choose Spellpower enchantments over mana regen enchantments, particularly if the mana regen is Spirit (i.e. Chest, Feet, and Wrists)
If you are not having any mana troubles, you may choose enchancements that give a bonus to crit or haste over mana regen (For instance, I use Arcanum of Burning Mysteries instead of Arcanum of Blissful Mending). This is perfectly fine.
If you primarily heal in 5 mans or (to a lesser degree) 10 mans, you are more likely to encounter mana problems, and I highly recommend you opt for mana regen enchantments.
You can also refer to Elitistjerks for their BiS enchants, as there are a few variations from my choices.
Standard Enchantments (Done by an Enchanter)
Greater Mana Restoration (420) (This is best for Holy Priests - if you are Holy, ignore the "Stats" to chest enchants. If you are Disc, do NOT get this enchant - you don't need it)
In addition, Enchanters may enchant their own rings with Greater Spellpower (you cannot have an enchanter do this for you, as it makes the item permanently soulbound). Arcanums (Headpiece Enhancements)
There is no enhancement for Neck, Trinkets, Off-Hand Items, or Wands, although Alchemists, Jewelcrafters, and Engineers can make their own trinkets, and obviously various professions can make different other items. Although this post is not intended to be a guide to which professions are best for the healing priest at end game, I would be remiss if I did not list some of the other item enhancements that different professions offer only for themselves. These profession specific item enhancements CANNOT be stacked with standard enchants, but are usually superior anyway.
Tailors have two Cloak embroidery options that are better than the Cloak Enchants:
Lightweave Embroidery - This is a pretty substantial increase to healing throughput, but I do not use it because you cannot rely on the increase when you need it. I won't notice that it procs, and just continue my job as usual (/shrug).
Darkglow Embroidery - I prefer this embroidery, as over the duration of a fight, it procs often enough (~35% proc, ~60s ICD) to give me a reliable "mana regen" boost. Good choice for priests, who use a lot of instant or short casts.
Springy Arachnoweave - The basic stats on this enchantment alone are much better than the haste enchants offered by Enchanters, even if you never use the parachute because you have Levitate.
Hyperspeed Accelerators - This is a fantastic haste increase, and really more like an extra trinket with a short cooldown. You can tie this to a macro and use it every ten seconds, or use it fairly regularly, and save the burst haste for when you are in a healing crisis and need to get a heal on someone ASAP. Does not activate GCD and stacks with other group/raid haste buffs (i.e. Heroism).
Nitro Boosts - Unless you are really desperate for mana regen, this is far superior to the crappy boot enchants. Also, the run speed increase can get you out of bad spots in a jiffy (zomg eyebeam), or if someone is stupidly out of your healing range and dying, get you closer to them to save their butts (I'm looking at you, mages!)