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While +healing gear will definitely help you, don't stress to much about it and definitely don't choose any over actual damage gear for your priest.
True, don't go out of your way for healing gear, but do keep an extra set of gear in case you are called upon to heal. You won't really need too much different stuff since the main stats at lower levels are int and spirit.
Once you hit 58 and enter the Outlands you will come across much better gear that has stats and +damage or +healing. This is when it becomes especially important to keep a separate set of gear as the instances also get harder. All I did was keep random drops that were an improvement to my healing gear and roll on BOPs in dungeons that were an improvement if no one else needed. Optimal is you as DPS and pally as healer so you can get most of the cloth healing gear and still roll on the DPS gear you really want. Doing it this way I actually got my hallowed set before oblivion (it just kept dropping!)
Get spirit tap for your first 5 talent points and try and keep a decent amount of spirit and you will solo just fine with the rare mana break after a while or if you pull multiple mobs.
Shadow priest is also much cooler looking than a mage or warlock and a lot more beloved by healers and mana DPSers alike. I'd say about 80% of the groups I'm in I get a "<3 Shadow Priests" whisper from someone. That rarely, if ever, happened when I was holy.
So, yes, priests are fun.