As a recent returnee after being away for a year+, I'd have to say I was shocked and surprised that I was still seeing green newbies in Sastasha (the very first grouped content in the game at Lv16 not counting Guildleves), the Original MSQ Raids (The very first ones) still have fast queue times, and even some fights after them like Leviathan, Moggle Mog, etc are all quick Q times as well.
I don't know about DPS queues, but Qing up for anything as a tank will get you a group within 5 minutes, and about the same as healer. In fact, even though the Duty Finder will claim Tanks are in need, I find more often than not, healers actually get faster queues, not sure why that is.
If you're worried about getting groups to get stuff done fast enough, I highly recommend you give tanking or healing a try. Healing will seem awful and boring at first, but once you get to about Haukke Manor, it starts picking up and you won't be so bored.
Aurum Vale will be your big Test. If you successfully heal that, you can probably heal nearly anything afterwards with a little practice.
Not everybody likes tanking or healing, though, so if you try it and you find it isn't for you, don't force yourself to do it. It's just that DPS will have longer queue times, and there's nothing I dislike more than waiting on the duty finder, lol. So I learned to tank and heal, right from the start.
EDIT:
I would also like to mention that most Grouped Content is done through something we call the Duty Finder. Basically, you tell it what you need to do (Dungeon, Raid, etc) while you have the job selected that you want to play as and it will place you in a queue which is shared with other servers.
When it is your turn to go, a popup window will pop and you click Ready when you're ready to go (you get like 45 seconds to respond) and when everybody in the group clicks Ready, you are instantly teleported to your Duty (you can't queue up for a dungeon you haven't been to the entrance of yet at least once, though. Dungeons and other Duties are unlocked by quests which almost always end at the entry point).
Once you're done with said duty, there'll be a glowing exit portal that you click once everything is done, and you are automatically teleported back to where you were when you entered the Duty.
There's also Duty Roulette, once per day you can get a huge XP bonus once you unlock it, basically it will pick any Random Duty that you have unlocked of that type and once you complete it, you'll receive a huge chunk of XP as the job you went as (regardless of what level the Duty was, you can do Lv16 Sastasha as a Lv50 and still get huge XP for it), which is why the Duty Finder population is so healthy, lots and lots of people doing their daily roulettes.
The Duty Finder also uses the Level Sync function, which means if you are a Lv60 and you get into a Sastasha group for your Roulette, you'll be temporarily lowered to Lv16-ish (20 IIRC?) until the end of the dungeon (similar to XI's Level Sync). This means that there are lots of opportunities to meet high level players even while you are a newbie, and learn from them, ask questions, etc if you need. I find that most people I meet are very reasonable and friendly though there are always bad apples occasionally. Usually, it's more the low level "I'll play MY way" type than the stuck-up high level from my experiences.
And what's cool, is that there are a lot of solo quest duties too... like mini-boss fights that you do solo, usually with NPCs helping you or other stuff going on. Some of them are rather cool and unique (like the WHM Lv50 one).
Edited, Jan 30th 2017 3:22pm by Lyrailis