Gear is very important in WoW. The main stats to look for on any piece of equipment are Intellect, Stamina and Spirit. Intellect should generally be your number 1 priority on gear. Try and get as big a mana pool as possible It will allow you to heal longer, and deal out more damage in solo play.
Spirit and Stamina should be your second priorities. It’s good to have high Spirit in certain situations (it helps with downtime when leveling, especially combined with Spirit Tap. It’s also good for long end-game raids), but generally, Spirit isn’t the best stat. Stamina is better, because with more hitpoints, you will survive longer.
Also good to look out for with the new patch are items that add to healing and damage. They are much improved, and now often come with other stats on the items. They can now compete with stat gear for spots.
Endgame Gear – Holy And Shadow
Endgame gear for Priests tends to be simple. Unlike other classes, you do not have access to anything other then cloth armor, so there's no need to mix and match gear the way shamans, paladins and druids can for the healing role. For the damage roll, shadow priests will be competing against warlocks and mages for similar drops, since all classes will be looking for +spell damage gear.

Holy
Head
Collar of Command – Shirrak the Dead Watcher, Auchenai Crypts
OR Watcher's Cowl – Ceneraion Expedition (Revered)
OR Hallowed Crown – Harbinger Skyriss, The Arcatraz
At first glance, the Collar of Command and Watcher's Cowl have superior stats to your class Dungeon 3 set. However, neither one comes with sockets, and with the proper gems the Hallowed Crown becomes a bit better than either one. Of the three, the easiest to get is probably the Watcher's Cowl – you'll be running a fair number of instances in Coilfang Reservoir, and because there are so many Cernarion Expedition quests in Outlands, its often the first faction you reach Revered with.
Neck
Choker of Fluid Thought – Harbinger Skyriss, Arcatraz
OR Living Ruby Pendant – Crafted
OR Ogre Slayer's Pendant – quest reward, Cho'war the Pillager
There are necks that offer more +healing, but usually at the cost of stats, and always the stamina stat. The problem with giving up stamina is that in raiding, there are several boss fights (such as the Shade of Aran), where having a certain number of HPs is mandatory to survive – in the case of Shade of Aran, you need over 8,000 HP after buffing, or you'll likely be killed by one of his spells. Therefore, these neck pieces offer a decent amount of stamina and still gives you a good amount of +healing.
Shoulder
Hallowed Pauldrons – Grandmaster Vorpil, Shadow Labyrinth
OR Vestia's Pauldrons of Inner Grace – Cache of the Legion, The Mechanar
Of the two, Vestia's Pauldrons are better, until you add gems to the Hallowed Pauldrons. However, The Hallowed Pauldrons allow you reach the set bonuses for that armor set, which are fairly useful. Of the two, you're more likely to see Vestia's Pauldrons first, since the Cache is easier to get to then Grandmaster Vorpil.

Back
Mantle of Vivification – Turning the Tide, Shattered Halls
OR Cloak of Scintillating Auras – Zereketh the Unbound, The Arcatraz
The two items are very similar, with the Cloak of Scintillating Auras swapping 2 Intellect and the the +7 mp/5 for +12 Sta, +18 Spirit and +2 more healing. Of the two, the Mantle is easier to get – it requires a quest item off the last boss in Shattered Halls, but is a guaranteed reward. However, I'd still try for the Cloak of Scintillating Auras when you are in the Arcatraz – the stamina can be useful, and your talents allow you to use some of the spirit for mana regeneration in combat.
Chest
Hallowed Garments – Murmur, Shadow Labryinth
OR Imbued Netherweave Robe – Crafted
OR Shroud of Spiritual Purity – BoE drop / AH
Of the three, the best choice is the Hallowed Garments – once socketed, it easily has more +healing then either of the other two items, and you can bring the stamina up to +24 or +30, depending on the gems you use. The Imbued Netherweave Robe is a good choice for fights like Shade of Aran where you want to get your stamina total up higher, but isn't the best everyday chestpiece. Finally, the Shourd of Spiritual Purity is a good everyday chest until you can get something like the Hallowed Garments.
Wrist
Shattrath Wraps – The Soul Devices, Shadow Labyrinth
OR Veteran's Mooncloth Cuffs - PVP
Wrist armor is one of the item choices where Blizzard did not plan properly. There's almost nothing to be had between green items of the physician and epic drops from Kara, crafting or PvP. This is one of the few areas I recommend PvPing, even if you don't enjoy it for its own sake, simply because PvP is the only place besides raiding that you can get a better upgrade. Aside from that, the Shattrath Wraps make good healing wrists, especially once a +healing gem is socketed into the red socket.

Hands
Hallowed Handwraps – Warchief Kargath Bladefist, The Shattered Halls
OR Prismatic Mittens of Mending – Commander Sarannis, The Botanica
It's something of a tossup between the two items – the Hallowed Handwraps are good for working towards your set bonus, the Prismatic Mittens offer higher stamina, int, healing and in-combat mana regen. Unless you have all four other pieces of your Hallowed set, I'd suggest using the Hallowed Handwraps.
Belt
Green Belt of the Physician
OR Veteran's Mooncloth Belt – PVP
OR Primal Mooncloth Belt - crafted
Remember what I said about wrist armor? The same thing holds true for belts. In this case, there really isn't a good blue belt in my opinion. Find the best belt of the Physician you can on the auction hall, but otherwise, you'll be looking at the Veteran's Mooncloth Belt from PVP or the crafted Primal Mooncloth Belt, although it has no stamina and low stats attached to it compared to the green item or the PVP belt.
Pants
Hallowed Trousers – Talon King Ikiss, Sethekk Halls
OR Pants of the Naaru – Special Delivery to Shattrath City, Netherstorm
The Hallowed Trousers are definitely a bit superior to the Pants of the Naaru, but the Pants of the Naaru are fairly easy to get, and come as part of the key quest for the Arcatraz. It's a tossup, and while both are good, ultimately I suggest working towards getting the Hallowed Trousers.
Feet
Jeweled Boots of Sanctification – Warbringer O'mrogg, The Shattered Halls
OR Veteran's Mooncloth Slippers – PVP
Feet are in the same boat as wrists and belt – luckily, there's a decent upgrade for your feet from Shattered Halls, unlike with belts. Still, if you have trouble getting an upgrade from raiding or heroics, definitely take a look at doing enough PvP for the PVP boots.

Rings
Keeper's Ring of Piety – Hero of the Brood, Caverns of Time
Ring of Convalescence – Revered, Honor Hold
Spiritualist's Mark of the Sha'tar – Battle of the Crimson Watch, Shadowmoon Valley
The Black Pearl (+33 Sta, +25 damage and healing) – Crafted
Rings tend to present you one stat and plenty of +healing – unfortunately, the stat isn't +Sta. Of the rings you can easily obtain, the Keeper's Ring of Piety and Ring of Convalescence will do well in your regular healing set, especially if you've been taking my advice and have plenty of stamina elsewhere. It's still good to have a The Black Pearl ring along for the huge amount of stamina on it, for fights where you'll still be taking some heavy hits.
Trinkets
Lower City Prayerbook – Revered, Lower City
Scarab of the Infinite Cycle – Aeonus, The Black Morass
Bangle of Endless Blessings – Warp Splinter, the Botanica
Of the three, the Lower City Prayerbook and the Scarab of the Infinite Cycle are the best for normal healing. The Bangle of Endless Blessings can be useful in allowing you more mana for longer fights by increasing your mana regeneration, as well as your damage and healing.
Weapons
Staff:Staff:
Epoch-Mender – Temporus, The Black Morass
OR Serpentcrest Life-Staff – Mekgineer Steamrigger, The Steamvault
Mace and Off-hand:Mace and Off-hand:Mace and Off-hand:Mace and Off-hand:
Hammer of the Penitent – Mechano-Lord Capacitus, The Mechanaar
OR Lightsworn Hammer – Warchief Kargath Bladefist, The Shattered Halls
AND
Lamp of Peaceful Repose – Dalliah the Doomsayer, The Arcatraz
As a priest, you can go one of two routes for your melee weapons – a staff, or a one-handed weapon and an off-hand. The difference is pretty simple – staves tend to give you higher base stats, while using a one-hander and an off-hand will give you higher +healing. Between the two staves, the Epoch Mender is the better choice if you can get it –

higher stamina and intellect stats, with only a little less effective +healing (due to your talent points granting a part of your spirit to damage and healing) and more in combat mana regen then the Serpentcrest Life-Staff. Between the maces, I recommend the Lightsworn Hammer over the Hammer of the Penitent – again, more stamina, intellect and in combat mana regen with only a little less plus healing.
Wand
Soul-Wand of the Aldor – Ambassador Hellmaw, Shadow Labyrinth
This wand is pretty much the best healing wand you can get before going to raid instances.

Shadow
Head
Crown of the Sea Witch – Crafted
OR Evoker's Helmet of the Second Sight – Teron Gorefind, I am..., Shadowmoon Valley
OR Mana-Etched Crown – Aeonus, The Black Morass
Of the three helmets, it's something of a tossup – The Crown of the Sea Witch will have the most stamina, but lacks the higher spell damage of the other two pieces, while the Evoker's Helmet can match the other two helmets in Stamina with stamina gems. My suggestion would be to pick up the Evoker's Helmet of the Second Sight, since the quests will also be worth a fair amount of money, and try to pick up two pieces of the Mana-Etched gear if you can, since the first set bonus is 35 spell hit rating, a nice boost to your attack spells, preventing NPCs from resisting your damage spells as often.
Neck
Brooch of Heightened Potential – Blackheart the Inciter, Shadow Labyrinth
OR Warp Engineer's Prismatic Chain – Mechano-Lord Capacitus, The Mechanar
The two items offer a lot of the same features – the Brooch trades some stamina, intellect and spell crit rating for a little more spell damage and some spell hit rating. I have no real recommendation either way – both are pretty good for doing damage.
Shoulder
Mana-Sphere Shoulderguards – Zereketh the Unbound, The Arcatraz
OR Mantle of Three Terrors – Chrono Lord Deja, The Black Morass
Once again, both shoulders are pretty equal – the Mantle trades the spirit and one point of int for more stamina and spell hit rating. Either one is a good option for your damage set, but my recommendation would be for the Mantle of Three Terrors if you can get it.

Chest
Vermillion Robes of the Dominant – Warlord Kalithresh, The Steamvaults
OR Robe of Oblivion – Murmur, Shadow Labyrinth
Once again, while the socketed item initially appears to be the weaker item, using the right gems can give it more stamina, slightly less int, and more spell damage then the other item. The gems also make it easier to use a helmet with a meta gem socket, if you are using one. Either way, both are good chest pieces to use.
Wrist
Shattrath Wraps – The Soul Devices, Shadow Labyrinth
OR Veteran's Silk Cuffs – PVP
As with the healing gear, there are very few blue options to upgrade your bracers with. The Shattrath Wraps are still the best non-PvP choice, since they can be upgraded with a spell damage gem as easily as with a healing gem. Otherwise, spend some time doing PvP for the Veteran's Silk Cuffs if you have trouble acquiring a bracer upgrade through raiding.
Hands
Energis Armwraps – High Botanist Freywinn, The Botanica
OR Jaedenfire Gloves of Annihilation – Ambassador Hellmaw, Shadow Labryinth
The two hand upgrades are nearly the same – the main difference is the Energis Armwraps offer their damage bonus to your holy spells and healing spells if you happen to cast those, while the Jaedenfire Gloves only affect your shadow spells. Because of this, I would recommend working for the Energis Armwraps, since they have more utility.
Belt
Sash of Serpentra – Warlord Kalithresh, The Steamvaults
OR Veteran's Silk Belt - PVP
Unlike with the healing gear, a decent belt for shadow priests is available from Warlord Kalithresh. You can also work towards the PVP Veteran's Silk Belt, which offers a decent upgrade across the board, but it isn't absolutely necessary.

Legs
Devil-Stitched Leggings – Laj, The Botanica
OR Incanter's Trousers – Talon King Ikiss, Sethekk Halls
Overall, the two trousres are near similar – the Devil-Stitched Leggings are possibly a little better due to the ability to socket them for different final results. Either of these two items is a good addition to your set however.
Feet
Silent Slippers of Meditation – Murmur, The Shadow Labyrinth
OR Veteran's Silk Footguards – PVP
The Veteran's armor in this case are more for the upgrade to your stamina total and spell crit rating then an across the board upgrade. If you enjoy PVPing, it's worth working for them, if you don't, focus on acquiring the Silent Slippers from Murmur.
Rings
Ryngo's Band of Ingenuity –Wrath-Scryer Soccothrates, The Arcatraz
Scintillating Coral Band – Hydromancer Thespia, The Steamvaults
Seal of the Exorcist – 50 Spirit Shards, Auchindoun bosses
The first two rings are roughly the same – they swap around stats a little bit, but they offer a lot of the same stats overall. The Seal of the Exorcist offers higher stamina, but no int. It does provide some spell hit rating, which is useful for landing your spells on higher-level enemies, like some dungeon bosses. It does require a lot of runs into Auchindoun while the Alliance controls the spirit towers, but overall it's fairly easy to pick up while you're trying for other gear from Auchindoun.

Trinkets
Vengeance of the Illidari (+26 spell crit rating, use for +120 spell damage for 15 seconds) – Overlord, Hellfire Peninsula
AND Starkiller's Bauble – The Horrors of Pollution, Netherstorm
Good spell damage trinkets are hard to come by outside raids and heroics – however, both of these are pretty good, with the Vengeance of the Illidari being hard to replace for a very long time.
Weapons
Staff:Staff:
Bloodfire Greatstaff – Aeonus, The Black Morass
OR Warpstaff of Arcanum – Warp Splinter, The Botanica
The two staves are pretty similar, with the Warpstaff trading some stamina and int for spell hit rating. They both provide the same amount of bonus damage, so whichever one you pick up first will serve you well. There's really no mainhand / offhand combination that matches either of these – most +spell damage one-handed weapons are swords, which paladins, mages and warlocks can use, but priests cannot. Once you get into heroics and Karazahn, your options open up more, but one-handed weapons simply do not provide the higher stats that a good staff does.
Gear For Advanced Player
Advanced players who want to pick their own gear will find this Kaliban's Gear Planner for Priest,
http://www.wowloot.com/gearguide.php?c=6
useful as it allows you to make your preference on stats and automatically calculates the total stat improvement for you.