If you haven't healed in previous versions, you're in a good place. A lot of the negativity of the healer camp right now is about what was changed from before. But not all.

WHM is straight forward, strong heals. Always has been. It's the easiest to pick up, IMO. 5.0 has a much better job gauge that's easy to use. They kitted us with some insta-heals and fixed a few weird abilities like Plenary Indulgence. DPS is also very good and Holy spam is as ridiculous as ever. WHM are very happy right now. You wouldn't be wrong to pick it.

SCH negativity is primarily focused on the loss of their DPS package from before. That was the draw for a lot of SCH mains. However, SCH is absolutely still a formidable healer that plays well. It's just not as DPS focused anymore. Plus the new Seraph is pretty rad. Fairy auto-healing makes a lot of dungeons a no-brainer. The fairy can heal most damage without a whole lot of player intervention.

AST negativity is pretty well deserved, IMO. The uniqueness of the card system was steamrollered and made cookie-cutter simple. There's very little decision making anymore. Just flat attack bonuses with short duration, so you're constantly having to throw them out. It keeps you really busy and requires several button presses at times (distracting you from healing and mechanics) and culminates in a pretty lackluster ability with a really long CD. The potencies of AST abilities seem a bit low, especially considering how much else they have to do for cards. Celestial Opposition in particular is pretty meh. It's the only healer with a ranged AOE though. It might be worth waiting to see if this class gets a patch soon...

Otherwise, a big difference between healers is the "type" of healing. WHM have good Regen and restorative healing, while SCH have shields for damage mitigation and the fairy for auto-healing. It's all healing, but they play and feel different. AST have the ability to swap stances and do either Regen or Shields.