If you really have zero experience healing and you don't know which class to choose, I strongly recommend a Priest. Paladins and Shaman are both highly specialized healing classes whereas Priests, while not the best at any one particular facet of healing, can do everything well. They have the widest range of healing spells and buffs, tools, etc. They really do have something for every occasion, and depending on how you spec you can specialize in either single-target tank healing (Disc) or cross-raid healing (Holy).
If Priest isn't your particular cup of tea, a Druid would be my second suggestion. They're also fairly well-rounded healers but they rely very heavily on HoTs compared to Priests' spells which are much more straightforward, direct heals for the most part. They're a little more complicated to play because of this, though no less effective. They bring a couple unique benefits to a party/raid in Innervate and an in-battle res as well in addition to their buffs.
Paladins are the best single-target healers in the game, which makes them phenominal raid healers at the end-game, but they're also the poorest multi-target healers which can make certain five-man instances, perticularly heriocs, a royal headache for them. They can provide passive auras to benefit their parties and a solid line of buffs.
Finally, you have the Resto Shaman, which I guess is me finally getting around to answering your original question. Shaman heal five-man instances slightly better than Paladins, but still not as well as Priests or Druids. In raids, they used to be considered the best cross-raid healers, but Holy Priests with Circle of Healing and Resto Druids with Wild Growth have taken that away from us for the most part. Shaman bring perhaps the widest range of buffs from a single source along with them; however, most of them can be provided by another class, so the wider the range of classes you stack around the Shaman, the more their value depreciates. Right now a Resto Shaman's main purpose, aside from providing their totem buffs and bringing Heroism, is to heal the melee stack around the tank. I dunno. It's kind of an awkward position anymore, to be honest...
Edited, Dec 21st 2008 12:26am by Gaudion