Of course, you can play any job in FFXIV and complete the main storyline, but there are canonical jobs for the story character as he/she swaps them during his/her adventures. I have collected them throughout the web and trailers, and here goes the list.
FFXIV: in the failed launch of the initial game, Warrior of Light was Archer.
FFXIV: A Realm Reborn. In the aftermath of the Calamity, where you start the current game (vanilla), WoL was wielding an axe, so finished the Ultima weapon and fled the false regicide accusations as a Warrior.
FFXIV: Heavensward. This one is easy, in a dragon themed and Ishgard based expansion Warrior of Light took up the spear and ended Nidhogg and Ilberd as a Dragoon.
FFXIV: Stormblood. This expansion is unique, as WoL sported two jobs on different continents. In Gyr Abania, WoL trained with Lyse and other monks of Rhalgr’s Reach, so he started the journey as a Monk. Upon travel to Far Eastern Othard, dealing with Yotsuyu and on, WoL learned the art of Samurai and had his final showdown with Elidibus at Ghimlyt Dark as such.
FFXIV: Shadowbringers. Obvious enough, as a bringer of darkness to a Light-swallowed world WoL explored the darkness in itself and coped with sin eaters as a Dark Knight.
FFXIV: Endwalker. Finally, to end Meteion’s song and save the planet the canonical job for WoL in the current expansion is Paladin.
Now it’s time to wonder what comes next :) As we see, all the jobs are either tanks or straightforward melee DPS which suits WoL serving as a tip of the spear for the Scions. My guess that next expansion he becomes Reaper… or another brand new job?
P.S. Trailer for Shadowbringers expansion shows this exact order of jobs as they came, expansion by expansion, during the fight with a sin eater as it breaks WoL weapons one by one :)