Here's a few pieces of gear and where to get them while leveling your priest or other caster class. Of course if you can get someone to run your through the low level instances, go as soon as you can.

0-10

Whatever greys you can find.

11-16

Whatever greens you can find, keep +healing gear it can really increase your value while grouping

17-20

The Deadmines

Complete the VanCleef quest line (Alliance only), it's long and sends you several places but you will receive [Staff of Westfall]

• [Lavishly Jeweled Ring]
• [Cookie's Stirring Rod]
• [Corsair's Overshirt]
• [Emberstone Staff]

24-27

• [Hands of Darkness] for Shadow Priests at level 24.
• [Wicked Moonstone Ring] (Shadow, L27) gives +6 bonus to shadow damage and +5 Intellect.

Blackfathom Deeps

• these almost always drop
  • [Rod of the Sleepwalker]
  • [Leech Pants]
• pick up In Search of Thaelrid which links to Blackfathom Villainy and you will receive [Gravestone Scepter].

Shadowfang Keep

• [Belt of Arugal]
• [Robes of Arugal]
• [Feline Mantle]
• [Odo's Ley Staff], though you may want to keep [Rod of the Sleepwalker]