I really disagree with the whole healers > tanks > dps idea. Basically the only time I stick to that (and even then quite loosely) is when I'm very new to a fight and unsure of my ability to keep myself/the party alive on my own. Every healer has the ability to solo heal everything that isn't Ultimate and that goes double for non-Savage stuff.

I tend to prioritize the strongest dps (not by job, I just keep an eye on the threat throughout and if more than one person is dead I'll stick to raising the one who was the highest first, it's pretty easy when I'm already looking at that for AST cards) with the exception of needing a certain person up for a certain mechanic.

Like oh, is there a dual tankbuster like in e1/e2? Well then if that might be coming up I'll raise a tank first. Is there a healer specific mechanic like in the Chaos fight that might confuse a tank or dps if they get it? I might raise my cohealer just to avoid that targeting someone else.

In general it pays off more to raise dps first, you're getting more damage out of your MP that way. Plus if a tank or healer actually manages to die with all the mitigation and restoration they have access to chances are they aren't exactly going to be performing amazingly for their role. Everyone has first times of course but that often isn't the case.

If you're unsure of your ability to carry raise a healer first if you really think you need to but you'd be surprised how little actual damage comes out in most casual content. It's literally the difference between (as a WHM) being able to heal with just lillies and oGCDs and having to occasionally toss a Medica 2 out or maybe Regen a tank.