All 3 healer classes are doing just fine in endgame, so your decision should be based on which playstyle you prefer.
WHM: strong heals, big aoe heals, several heal over time effects (regen), decent dmg, but generally a bit slow.
SCH: uses shields to mitigate dmg before it hits, weakest heals out of the 3 unless Atherflow stacks are available (3 per minute) which give access to strong instant heals. Thanks to the fairy, SCH spends most of its time as a DPS.
AST: uses shields or regen, depending on stance, but both are a little bit weaker then their respective aequivalents. Has a wide variety of support skills which the others lack and the quickest normal heals + 1 small instant heal, but kind of sucks at dealing dmg (especially pre-52) in comparison to the others.
Cross-Class Actions you need are dependent on which healer class you pick:
WHM: Virus (12) and Eye for an Eye (34) from Arcanist, Surecast (8) and Swiftcast (26) from Thaumaturge.
SCH: Aero (4), Cleric Stance (6), Protect (8) and Stoneskin (34) from Conjurer as well as Swiftcast from Thaumaturge.
AST: Cleric Stance, Protect and Stoneskin from Conjurer, Surecast and Swiftcast from Thaumaturge.
If you’re as new to healing as you say, you have two options:
First would be going for whichever job seems the most appealing to you.
Secondly would be to pay heed to learning curves.
If you pick the first option, you’ll need to be aware of the more popular healing meta: One healer does most of the healing, the other spends more time contributing to damage and/or mechanics. This does not mean that one healer’s solo healing and the other’s a pseudo DPS job, however. I’ll refer these roles to main healer and support healer for the rest of the post.
White Mage has high affinity for the main healer seat. Their kit is mostly about healing and the DPS tools are all tied to accuracy issues and are rather GCD inefficient. They’re a poor choice for the support healer spot.
Scholars as decent affinity towards the main healer seat. While they’re not “terrible” to take the major brunt of the healing, their access to burst healing is reliant on abilities. Some of these abilities are tied to Aetherflow as well. But they have the strongest affinity as a support healer. Unlike White Mage, Scholars have three attack spells that aren’t tied to accuracy. But the main selling point would be the on-demand mitigation Scholars can provide. For both single target (tanks) as well as whole groups.
Astrologian can fulfill both roles, but fits the main healer seat the best. Simply because their on-demand mitigation is nowhere as good as Scholar and their offensive spells are rather MP inefficient. The bread and butter healing spells are very similar to White Mage, however. Additionally, Combust and Combust II aren’t tied to accuracy and have a combined potency of 690 for 2 GCDs (345/GCD). Scholars have 1140 potency for their 4 DoTs (285/GCD) and White mage 820 potency for their 3 DoTs (273/GCD). It’s a different story when it comes to multiple targets, but let’s omit that for now till you’re more familiar with the role itself.
There’s also the thing that a part of the community expects some damage contribution from their healers. Even more so for 8-player content. Opinion differs for 4-player content.
If you’re going for the second option, you’ll want to level a Conjurer/White Mage first. Because:
1) You’ll need to take it to 34 for Stoneskin anyway
2) Conjurer/White Mage is a bare bones healer till you hit the wall called endgame.
Don’t get me wrong, White Mage is a healer and is really good at it. But while leveling you can get away with just learning to heal while other jobs:
Astrologian cards may distract you from learning the role as a healer
The fairy takes a brunt of your job as a Scholar in low level dungeons – It may seem appealing to afk-follow the tank while leveling, please don’t do this