The best bet is Conjurer or Thaumaturge main with sub abilities from whichever isn't your main for healing. Conjurer's cure is an AOE cure while Thaumaturge has a cone heal that damages themselves to heal others. Conjurer's cure as a sub ability is single target I believe and not AOE. You can experiment with both to try to find the combination that fits you best.
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Be wary of the "loaded question" responses or "use the search" around here. Welcome to MMORPG though.
Conjurer is going to have primary healing (Cure/Raise) abilities but so will Thaumaturge. Now that is the basic answer.
The deeper answer is any class due to being able to combine abiltities from any class with your current one.
Meaning, you could create a Paladin type character if you wanted using Gladiator, Pugilist and Conjurer skills.
You can look at class skills here: http://ffxiv.yg.com/
Assuming you have been to main site for general information on Armoury system it is here for reference:
http://na.finalfantasyxiv.com/
The best bet is Conjurer or Thaumaturge main with sub abilities from whichever isn't your main for healing. Conjurer's cure is an AOE cure while Thaumaturge has a cone heal that damages themselves to heal others. Conjurer's cure as a sub ability is single target I believe and not AOE. You can experiment with both to try to find the combination that fits you best.