WHM is a fantastic choice for dungeons because Holy is just so good but if you want to learn how to properly heal while dpsing instead of the classic "I'll just heal everyone first and then maybe dps a bit", WHM mostly teaches bad habits because its toolkit is so barebone you have to use a lot of GCD heals. Far more often and for much longer than the other two. As beginner friendly as it looks, it's actually strongest in the hands of very experienced healers and not particulary good or easy to handle for a starter healer because healing and dpsing is mutually exclusive for a long time.
If you struggle with getting rid off the GCD heal habit, WHM will shove it right back down your throat.
SCH has far less target switching than AST because your instant aoe is centered around you, not targeted. So you can just keep targeting the tank while doing your thing. It's a bit more busy and has more buttons because you have a larger toolkit but managable. It's very easy to get used to GCD dpsing and oGCD healing on SCH.
And the fairy auto heal makes it a bit more forgiving than the other two because it's like a permanent regen on (mostly) the tank.
AST is the busiest healer with frequent target switching because of Gravity being targeted but remember that while cards are good, you can gradually incorporate them as you get more used to target switching on controller. So if you fail at cards at first and card the wrong person, it's not the end of the world. Chose your battles and set your priorities correctly, then you can go for AST aswell. You'll only run into problems if you want to nail everything at once.
Just like SCH, the free weaves make it easier to practice GCD dpsing while oGCD healing and slidecasting is more forgiving. But it will require more target switching than WHM or SCH in mass pulls even if you don't focus on cards at first.