Rage Quitting this game

[Tigore]

As others have said, it will help a lot if you take it easy with the low level dungeons first as a new player. The higher dungeons will start to expect healing cooldowns that use no mana, but restore a decent amount of health. A certain gear item level is also expected, so we need to make sure we get new gear whenever we can. Try to aim to keep the gear around your class level the best you can.

If it's possible, maybe try out the Conjurer / White Mage class for a bit to get comfy with the basic spells first. Satasha will start off with mostly using just Cure and Medica (or Benefic and Helios with Astrologian). I believe the cooldown Lucid Dreaming comes up fairly soon and that one is important to use when you drop to around 80% of your mana or lower. It contributes a lot of mana regeneration, so make a habit of using it whenever you can. Then when you get to level 30, don't forget to visit the class guild again to upgrade your class to a job class. It then sends you on job quests to earn spells that will be important to use. An example is Regen that appears for White Mage at level 35. That one gets put on the tank(s) as often as possible after they finish pulling enemies to heal them over time (a HoT for a short term). Try your best to wait for the tank to finish pulling before using the HoT heals or the enemies might potentially start chasing you if the tank accidentally didn't hit them all yet. Astrologian can use the Diurnal Sect buff and Aspected Benefic to get a similar regen too.

[Rilifane]

I agree that maybe you could start looking into tanks.
If you fail a mechanic you barely take damage and get a vuln stack in later dungeons but I've kept tanks alive that collected 5+ of them through tankbusters and they didn't even bother to use a cooldown. For the most parts, trash is "pull as much as you're comfortable with, use some cooldowns, don't stand in the orange" and bosses are "face away from group, don't stand in orange". If you don't recognize a mechanic, imitating what others are doing generally works and if it doesn't, it won't kill you.
You don't have to know every nook and cranny of a dungeon as some people say, that's nonsense. They're linear enough that it's hard to get lost and even if you took a wrong turn, you just run back.

You can always come back to healer if you want. But they're more dependant on other people's performance and if they die, they fight is usually over unless you either have a RDM/ SMN who can ress you (and hopefully in time) or a PLD who can keep himself alive.
Besides, AST is not exactly a good choice for someone who gets stressed out by what's happening pretty fast or hasn't played in a long time. Boosting it would be a terrible idea because you don't have time to get used to your skills. If you really want to keep healing, it might be best to stick to SCH or WHM for now. AST is even more dependant on decent group play than the other healers.

[Yuella]

Sounds crazy but I always tell people play tank. Its the easiest role in the game for regular lvling content. You can face tank alot of mechanics and survive. You dont need to memorize alot of things because its the dpses job. You dont have to keep your butt alive as well as cover for others stepping on aoe like healers do and the queues are great.

Healer to me is the hardest because you are basically the backbone of the team that smooths over others mistakes by healing them through it. I dont really like healing at all since the potency/ dps nerf.

Parties sometimes want tanks to pull big and newcomers may not be comfortable with it

[Rilifane]

Parties sometimes want tanks to pull big and newcomers may not be comfortable with it

Parties sometimes want healers to dps and newcomers may not be comfortable with it.
Parties sometimes want good aoe rotations and newcomers may not be comfortable with it.
If you don't want to pull big, tell them. They'll either leave it at that (most likely) or kick you (rarely happens because getting a new tank takes longer than finishing a dungeon with single pulls). This whole "they may want this or that and it could be uncomfortable for you" is just needlessly feeding "tankxiety". Just like all this talk about how a tank needs to know the whole dungeon by heart, lead the way, know how capable a party is at a glance etc.
There will always be players that want a different playstyle from you regardless of role. But the solution to that is really quite easy: communicate. It's not that difficult to simply tell your party that you're not quite used to tanking yet and will keep pulls smaller. I honestly can't remember someone ever getting salty over it or even demand a kick.
The general reaction is as simple as "ok".

[magdahmhara]

If you want to heal go white mage if you want to dps go machinist. Both easy to play. When healing what i did was just queue for dungeons normal don't use roulette. Pick lower level ones till you get comfortable and move upwards one at a time. Skip aurum vale unless you are doing it with friends, lol. Yes dungeons do get progressively harder starting with stone vigil. Some dungeon mechanics usually end up in other dungeons so if you are familiar with them it gets easier. Healer is a stressful job because you feel like if you mess up everyone will get angry at you. Just tell them you are new at the very beginning and could the tank please not over pull till you are comfortable. If have found when you are honest with the group up front before a wipe happens most people are cool about it. I had a friend that kept telling me "this isn't WoW", lol. It took a very long time to get over the fear of toxic attitudes from years of that game. Anyway, relax and have fun. That's what games are for. Hope you find your place here.