Thanks to @tzenes for an ElitistJerks link, which has some great info. Of note is that Shadow Word: Death is much better than it used to be.
Summary:
- No specific information on how to start the fight
- Keep up Vampiric Touch, Devouring Plague, and Shadow Word: Pain
- Shadow Word: Death when available
- Mind Blast when available
- Mind Flay for filler
One important note is that (with a Glyph) Shadow Word: Death has an instant cooldown when the boss is below 25%. This means you'll need relatively little Mind Flay filler past the 25% mark. Just don't kill yourself.
I am going to suspect that Mind Blast could eventually outperform Shadow Word: Death later on, especially with Mastery points making it more effective and Mind Spike synergy. But according to Elitist Jerks, Mastery is pretty terrible at the moment.
First off: I would warn against basing any decision like this on month to month balance considerations. Things change so often in WoW that you should really decide based on how much you enjoy a particular classes playstyle, toolbox, and yes, even aesthetics. Healing Balance is Pretty Good right now. All five healing specs have a role to play, and a (25 man) raid which doesn't have the flexibility to see them all represented is a 25 man raid that is going to run into trouble. At the five man level, all five specs are more than capable of handling any content you'll see, though Discipline Priests in particular may find Heroics somewhat more challenging than most due to increased gear dependency.
That said, the current state of PvE healer balance at the high end is this: Priests are somewhat above average at Group and Raid healing - this is reflected by the nerfs to Prayer of Healing in the upcoming 4.0.6 patch, but those nerfs don't really change the overall state of things. Additionally, Priests bring extremely powerful cooldowns to a group such as Pain Suppression, Guardian Spirit, Leap of Faith, Divine Hymn, and Power Word: Barrier, all of which are defining abilities that have had entire strategies built around them. If you see raids specifically looking for Priests to heal, this is why.
Shaman by contrast, are currently the kings of PvP healing because they are extremely durable, mobile thanks to the new Spiritwalker's Grace ability, and bring substantially more offensive utility than other healers thanks to Heroism/Bloodlust, Wind Shear, Totems and Purge. In PvE, every 25 man raid wants at least one Resto Shaman for Mana Tide - and 10 mans love to have it as well. Mana Tide is the single most powerful mana regen ability in the game, and it is absolutely essential for success for many groups in many encounters. Additionally, you may find it easier to gear up a Shaman for healing because there will be less competition on mail pieces with intellect than you will find on similar cloth pieces - and because if you already have decent DPS gear, you always have the option of DPSing your way to a healing set.
My advice to you? Try out healing on the shaman. Chain Heal, Spiritwalkers Grace, Riptide and Healing Rain are all enormously fun abilities, and the Shaman healing style is unique among healers in WoW. Unless you're pushing bleeding edge content the class balance issues seen there are going to be largely moot for you - what matters much more is your own competence and gear.
As an aside, checking the WoW forums will always find you nothing but gripes. A saying I'm fond of is that the forums are as much an indicator of players happiness as a hospital is an indicator of public health.
Best Answer
Pulling a lot of mobs for leveling is a rather bad idea when playing solo as a cloth class. You are too squishy to effectively tank 5+ enemies without cooldown usage.
Now while I'd recommend you to pull single mobs when leveling, you can still try to grind your way up to level 100 by killing multiple NPCs at the same time but there are some things you should keep in mind.
Talents
An important thing to note is that the talents for leveling are different. While you would usually pick up Insanity as your level 45 talent in a raid, you should pick Surge of Darkness when you are soloing quests etc. Mainly because of the extra burst you'll get.
Crowd Control
Something that also should be mentioned is Crowd Control. Yes I know. Priests aren't hunters with 30 traps and slows but you should make use of the spells you've got. Try to Fear enemies who get too close with Psychic Scream while also kiting dangerous melee mobs. Basically just try to avoid as much damage as possible.
Single vs. Multitarget
While leveling you should generally focus on singletarget damage. Even if you're pulling a lot of NPCs it's usually better to focus them down one by one instead of trying an AOE rotation. (I acutally think Tank roles and DPS warriors are the only classes that can really pull 10 NPCs or more while still clearing them quickly without dying). The shadow priest has some nice burst potential. You can usually kill a NPC with
While of course looking out for procs which allow for even more burst. (Vampiric touch isn't really too good while leveling)
If you're fighting a lot of enemies you can multidot with your Shadow Word Pain but you should still have one focus target. Also always use your Devouring Plague on cooldown.
(Defensive) Cooldowns and Selfheal
Every class has Cooldowns and a SP even has quite a lot of healing potential. Don't hesitate to use your CDs. 5 minutes recharge time aren't a lot while leveling. Especially not if it lets you kill stuff faster. Use Offensive and Defensive cooldowns as often as possible. If you're taking too much damage, use your dispersion and run away or Shield yourself. If you're low on health CC the enemies and start healing yourself.
If you follow these steps you won't die that often. But remember everyone can die while leveling. You can accidentally pull too many NPCs or ignore a certain mechanic that an enemy has. Cloth classes just aren't made for tanking a lot of NPCs.