You won't get kicked from dungeons just for being new. At low levels people tend to be pretty understanding, and most of the ones I've seen will help new players learn how to play their class/job. At max level they get less forgiving, but seriously by that point you've had 60 levels to figure it out.
"Easiest" is going to mean something different for you than it does for me, so I can't really answer that question. My recommendation is to try a variety of classes and see what appeals to you. You might also look up some gameplay videos of the jobs being played at high levels to see if anything grabs your interest specifically. Don't worry about complex rotations right now, plenty of time for that. Just look for a job that appeals to you and seems like it would be fun to play. Every job is viable at all levels of play so there's no wrong answer here.. just pick the one you enjoy (or the one that looks the coolest and makes you want to learn it).
EDIT:
If it helps at all, here's a quick table of what each job's role is so you can look things up more easily.
Tank (job is to get punched in the face and not die): Marauder/Warrior, Gladiator/Paladin, Dark Knight
Healer (job is to make health bars go up): Conjurer/White Mage, Arcanist/Scholar, Astrologian
Melee DPS (stabby stabby): Pugilist/Monk, Rogue/Ninja, Lancer/Dragoon
Ranged DPS (pew pew): Thaumaturge/Black Mage, Archer/Bard, Arcanist/Summoner, Machinist
Dark Knight, Astrologian, and Machinist are not available until you reach the Heavensward story, they're just included here for completeness' sake. Arcanist is listed twice because it actually becomes two different jobs.
Edited, Feb 17th 2016 10:00pm by Callinon
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svlyons wrote:
If random outcomes aren't acceptable to you, then don't play with random people.