Holy is by far the best healing spec.
You can choose any spec you want, but for most 5-man dungeons above level 50 or so, a Holy priest will have by far the best healing. I have a level 70 Holy priest and with enough spell damage gear, you can do decent damage, just not very fast and much less than Shadow or Discipline, usually.
I would play Shadow up to about level 50 or so and then switch to Holy for dungeons. If you get in a raiding guild with lots of healers, but few Shadow priests you can stick to Shadow, because it is usually good to have 1 or 2 Shadow priests in a raid for group HoT (heal over time) and mana regen.
You pretty much only play Discipline at higher levels for PvP. However, I've heard you can solo decently, so maybe you could try Discipline instead of Shadow at lower levels.
The best way to do damage as a Holy priest is to make sure you have a spell damage set of gear (for soloing mostly) for those situations where you can get by with less than your best healing. However, you will want to have your best gear be healing gear.
Don't worry too much about switching to and learning how to play Holy spec until after level 50. Before that you will be changing gear every 2-3 levels and won't really want to spend much time and money on gear. Some people don't worry until they're level 70.