A shadow priests job in a raid is more or less singular; Vampiric Touch. You are a mana battery. Vampiric Embrace is helpfull as well, but there are some fights that you probably wont even use it in order to conserve mana. Vampiric Touch though doesn’t do much if you can’t do shadow damage, so damage is important as well. Shadow Priests are not Warlocks though, we don’t do 10,000 crits, and you never will, so dont loose site of your purpose while chasing warlocks and mages in the damage meters.
So, that said; priorities. Spell Hit, and Spell Power. If you can’t hit your target, most any other stat is useless, so spell hit should be your number one priority. Since this guide revolves around kara, we’ll assume your targets are all level 73. Assuming you put 5/5 in Shadow Focus, you’ll have a 96% chance to hit a boss as your base. Which means you need about 71 more +hit in order to have a 99% chance to hit. Second on your list is your shadow spellpower. As far as I know there is no cap on this, so take as much as you possibly can.
Items with a strikethru mean I’ve been able to get it for my shadow priest [Sinisha] 
Crafted Items
You could theoretically have all of these items before you even get attuned for kara, although its not likely. Personally, I didn’t have any, and I only had the shoulders the first time I did a raid.
[Frozen Shadoweave Shoulders]
[Frozen Shadoweave Boots]
[Frozen Shadoweave Robe]
[Spellstrike Hood]
[Spellstrike Pants]
[Girdle of Ruination]
Karazan Loot
[Bands of Nefarious Deeds] (Maiden of Virtue)
[Handwraps of Flowing Thought] (Attumen the Huntsman)
[Ritssyn's Lost Pendant] (Trash Mob)
[Shadow-Cloak of Dalaran] (Moroes)
[Staff of Infinite Mysteries]1 (The Curator)
[Ring of Recurrence] (Chess Event)
Purchased Items
[Carved Witch Doctors Stick] (25 
)
[Icon of the Silver Crescent](41 )
Quest Rewards
[Darkmoon Card: Crusade]
[Violet Signet of the Archmage]
Without any gems, or enchants the base stats (that we care about) of all the above gear comes out to
- Spell Hit: 75 (99% chance to hit any target)
- Shadow Dmg: Gear alone puts you at ~830, add in the darkmoon proc, trinket use and shadowform and your looking at something around 1200 shadow damage.
- Armor: 1137 base (15% mitigation), around 2700 buffed (30% mitigation)
- Intellect: 244 unbuffed
- Stamina: 313 unbuffed, 425 with fort buff
Gems
[Don Julio's Heart] (if your a jewlcrafter)
[Runed Crimson Spinel]
[Runed Ornate Ruby] (6,885 
)
[Runed Living Ruby]
Notes
1. Optionally if you have the honor, or can’t seem to win the rolls you could get the [Gladiator's War Staff] instead. Or obviously, even better the [Merciless Gladiator's War Staff]. But with the spec and gear listed here, you’ll have a tough time with PvP.