What I'm looking forward to level, in no particular order:

Gunbreaker - Because gunblades are cool.
Paladin - Always liked the sword n' board aesthetic. Wasn't too much of a fan of spamming a spell with a cast time, in a small buff window, as a tank.
Warrior - Mostly just because I like using Fell Cleave, or spamming Steel Cyclone in a huge pack of mobs, and seeing all those healing numbers.
White Mage - Really feels like the iconic Final Fantasy healing job to me. That, and Holy spam + Assize.
Dragoon - Been a fan of the job aesthetic for a long time, especially the type of weapon used.
Red Mage - I like the idea of combining melee with magic, even if it's mostly magic in XIV. It's also a pretty relaxing job, for those moments when I don't want to think too much about rotations.

Jobs that I'll likely check out after the above ones:

Dark Knight - Wasn't a fan of the Dark Arts spam, but curious how it'll be in Shadowbringers.
Ninja/Samurai - Sorta like the more Eastern themed aesthetic, but these two jobs don't do much for me past that. Also not a fan of the Mudra system due to ping.
Black Mage - Blowing stuff up with big, fiery explosions can be fun, but Leylines gave me Rune of Power flashbacks.
Summoner - Books as a weapon seem kinda boring, although the rework coming in Shadowbringers looks interesting.
Machinist - Like the aesthetic, wasn't a fan of the skill design of Stormblood.
Bard - Like classes that use a bow.

Jobs that don't really interest me too much (but will level anyway, for completion's sake):

Scholar/Astrologian/Monk - Job aesthetics just don't do much for me.