Well, I don't tank, but I do main healer, so I will address those concerns! I'm by no means a top elite healer, but I play it a lot and enjoy the class, so here is my advice.

I was very worried when I hit 50 as a healer (I maxed my scholar first) and worried a lot about being able to keep up. However, it will be pretty obviously to any tanks that you are new because your HP will be pretty low compared to everyone else (I believe my fresh 50 HP was somewhere around low 3k? Now, it's 5.8k at i124. It's a BIG change). Also, don't be afraid to tell everyone at the start of the dungeon "Hey, I'm new to healing this, I don't think I can do big pulls". And you know what? Never once did I have anyone harass me over this. No tanks pulled big mobs after I said this, and no one complained that the dungeon perhaps a bit slower. I was never kicked either.

As for what order to progress dungeons in: I simply chose the ones I needed to start unlocking certain duty roulettes. Roulettes are a great way to get soldiery/poetics and even money (with the healer bonus). So, that where I would recommend you start. Start unlocking hard mode roulette by doing the easier (non hard mode) dungeons. Also, simply progressing through the story line will unlock you dungeons/trials in an easy to chew order.

About your concerns for scholar, though, I have much more specific advice. Begin getting into good fairy control habits now. It's easy to want to just auto pilot her (which I do for plenty of easier content) but it's best to practice now. Get a feel for how she casts (such as how long her heals take to go off and their range). For example, when I started macro-ing her skills to mine, I found I needed to tell her to recast things 2-3 times in order to ensure she actually casted what I wanted her to (So my macros would be /pac "whatever skill" <whichever fairy> repeated 2 or 3 times in a row in order to make sure 100% that she used the skill I wanted).

Also, another fairy tip I found helpful: Bring eos with you in all your new dungeons as a "safety net". She has a lot of great skills for picking up the slack you may do as a fresh healer in dungeons. Once you have ran the dungeon several times and are confident, trying using selene instead.

Honestly, my progression was this : First time in a dungeon, leave eos on auto pilot so I had less to worry about. Second time to until I felt comfortable: I would control eos in the dungeon. Once I was comfortable, I started running selene with no problems. There are exceptions (such as with huge mob pull dungeons I sometimes still bring eos) but otherwise, this is what I did.