The Paladin gets respectable self heals, by healing others.
As her own Beacon target, she can put out very strong self healing.
Bubble makes her immune to attacks for a short duration, except that a few classes can end that early; but she is a poor target for most compositions because of the bubble.
With cooldowns, her heal throughput is amazing.
Resistance Aura and Blessing of Kings are both strong buffs.
In 5's, you know the healer is going to be focused hard and fast.
They wear plate and carry shields.

The Priest has two healing specs.
Discipline used to rock, but isn't that great in the 4.0.1 game; not sure how it will be in 4.0.6
Holy has the ability to continue to heal, for a while after dying.
If your initial target has an immunity effect like a bubble, mass dispel ends that... making the priest a stronger offensive choice to help ensure the first kill target dies while you have the cooldowns up.
You can Fear Ward the first fear, and have an AoE fear too.
Fortitude is a decent buff.
A priest is relatively squishy in cloth.

The Shaman is an interesting choice.
Earth Shield helps to keep her alive.
The totems offer a lot of buffs, including the equivalent to the Paladin's resistance aura.
Tremor is now a party trinket for sleep/charm/fear effects.
You have Heroism/Bloodlust in battlegrounds, but no longer in arena.
Purge has been nerfed a bit, but you can still remove opposition buffs, which can make an impact.
Shammies wear mail and carry shields.

I like a druid healer quite a bit, but not so much with relatively little attention given the toon.
Initially she would be stealthed, which until you need heals is the strongest defense option for any of the healers... provided you are okay with them coming to you, or you moving slowly.
Innervate can be purged/spell-stolen/etc, but doesn't nerf the heal output and is less vulnerable than a Mana Tide.
Barkskin + Tranquility is probably the best AoE healing, although others are good too.
The class is dependent on HOTs on the target, so there is a ramp up time.
Tree Form is a major cooldown, for serious heal through-put.
Mark of the Wild, is the same as Blessing of Kings now; a scaling buff as your team gears up.
The class wears leather, and no shield.




Whatever you go with, is probably workable.
Each has its own strengths and weaknesses, at least in comparison to the others.

Once a healer toon is noticed, any smart opposition will focus you.
So the ability to survive while focused is a strong consideration.
Chances are you'll be focused sooner in arena than in world or battleground pvp.

A large part of this team is managing your cooldowns.
The DPS is one button spam.
But you have Icebound Fortitude, Pillar of Frost, Anti-magic Shield, Lichborne, etc to manage.
The less you have to do, to keep the team alive... the more you can automate the healing the better.

Mosg2 has a pair of macros which really spam Focus target with a lot of healing.
The focus can be changed relatively easily.
And the special abilities are mostly off of the GCD.
Being able to set up your healer in a similar manner will be a major plus.