I may not have played a priest but I wore almost all priest gear on my druid. When I choose gear for a character I normally try to max out one stat that will make me extremely powerful. Healing gear is very different. There are three stats that are crucial for a good priest: Intellect, Spirit, and Healing Power. I personally like to balance these stats so they are all strong. Of course it's up to you what you prefer to focus on so I will go over what each stat does for you.
Intellect: This will boost your maximum mana and increase your critical heal chances. If you have a huge amount of mana, naturally you can use more heals before running out. I don't put much faith in critical heal chance, because it's a random thing that you really can't rely on. You just occasionally get a heal for a huge amount of bonus health. It's a nice bonus to increased intellect though.
Spirit: This dictates how much mana you regenerate over time. When you aren't casting heals, your mana naturally regenerates slowly. Increasing spirit increases the amount of mana you recover every tick (5 seconds or so). This won't regenerate nearly as much while casting so it's better for players like myself who like to rely on casting a whole bunch of healing over time heals then backing off for a few seconds to recover mana. My druid had enough spirit that I could keep low to medium levels of healing constantly going and actually end a battle with more mana than I started.
Healing Power: Some rarer items will give you +Healing. This makes every single heal you do heal for more hp. The power increased depends on the cast time of the heals. Overall you will notice a boost in your healing power when you get more of these +healing items. If you get enough +healing to your attacks, they will do enough healing that you can actually use a lower rank heal to do the same healing power. For example I had about +1300 healing power on my druid. This made his heal rank 8 about as powerful as a normal heal rank 13. Instead of using the rank 13 heal for a huge amount of mana, I used the rank 8 version for much less mana. This is especially nice when you can use a rank 1 or 2 spell which usually casts faster than the higher ranks.
As a low level priest, I would go for mostly intellect, and perhaps some spirit. As you grow you might want to put more into spirit and +healing towards the higher levels. I personally prefer armor that has intellect and spirit on it. If you search for green armor "of the owl", you will find armor with boosted int and spirit together. "Of intellect" will also boost your int a little more than "Of the owl" but not by much more. For example, a green tunic of intellect may have about +4 int, and its of the owl counterpart will have +3 int, +3 spirit. So shopping on AH, I just type in "of the owl" into the search field and pick up whatever I can that's close to my level.
If you get good enough stats, your mana will last a lot longer and you will be able to keep your group alive much longer.