You will find that the priest will have the most supportive tools along with healing, and the most straight forward healing apart from a pally.

Priest's heals are basically 2 AoE heals, a HoT, and several types of straight heals that will heal for certain amounts. has a shield that will help absorb damage, and can heal after death (but you have to be controlling to priest to actaully get this to work, unless im doing this wrong). there's also lightwell, i believe, that allows you to place a thing somewhere and people have to click on it to heal (i personally think its useless).
Druid heals are a bit more complex. There is one Hot, one that starts as a HoT but ends with a burst heal (lifebloom - and can be postponed indefinitely by renewing the spell before it ends), a heal that starts off as a straight heal but also adds a HOT after the heal (regrowth). There is an AoE heal called tranquility. tree of life form rocks. lower mana pool than a priest, though has and Evocate-lke spell which i forgot the name to. Last thing that would have me going for druid is the OOC rez and the In-combat rez. wonderful just in case the tank dies. dont forget you'll last a lot longer when you draw aggro by turning into a bear. i like druids more. but you might enjoy the tools you get as a priest as well as a shammy.

For the Shammy, i'll let the many shammys in this forum tackle that. =]


edit: one other thing i might wanna mention is that if you can balance out the spec's right, you can do both dps and healing from certain classes. 4 boomkins +heals, or 4 shammy dps +heals will also work and can greatly simplify your spell rotations and also helps to distribute threat to every shammy/druid.