Level them all to 60 and play them all ^_^ That would be my generic advice. Healer gear is kind of....generic, and secondary stats are a bit meh except for SCH and crit (even then it's not the end of the world).

Healing end-game content is never single target cure/physic/benefic spam though it might feel like that at the moment around the level 50 range.

Based on your thoughts I'd recommend going WHM first, then SCH and AST last (if you were prioritizing levelling).
WHM will lay some good solid foundations for pure healing with a touch of stance dancing.
SCH will give you a bit more experience on healer DPS.
AST is a support role, and you don't seem to enjoy the cards. Cards are quite a distraction and if you don't like them it is probably not the role to play.