Another New Player thread:

[Bixby]

For leveling any battle class (healers and tanks included), I'd advise taking advantage of everything the game has to offer. Hunting log, challenge log, side quests, levequests, FATEs, guildhests & dungeons (and their roulettes). I find it feels a heck of a lot less grindy if I keep doing different things. Levequests are a bit of a last resort for me, because the XP is just not that great for battle classes, and the allowances are better saved for gatherers/crafters. But I'll still do them now and then when I have allowances to burn & don't feel like the other options.

Regardless, they all level fairly quickly these days. It's just a matter of which sort of leveling you lean toward on which role. Saving quests for DPS classes isn't a bad idea, though.

Something you might consider, just for right now, is getting your CNJ up to the level of the first few dungeons, and then pausing to switch to ACN or THM. On the 28th, we're getting patch 2.4, which is bringing in Rogue as a new class (with Ninja as its job). If you like dungeons, that will be prime time to be leveling a healer, because Rogue/Ninja is going to be DPS, and everybody and their dog is going to be leveling it, which means queue times for tanks and healers are going to be even better than usual. Normally, you'll have instant queues as a healer up to level 30 (when Scholars start taking some of the healer slots), and after that they taper down to midway between DPS times and tank times. I'm guessing that bump at 30 is going to get much smaller for a while starting on Tuesday.

Tuesday is probably also going to mean a ton of Rogue/Ninjas grinding FATEs while they're waiting on dungeon queues, so it'll also be a good time to join the FATE zerg for a while, on any class.