Should I max Lancer before starting Dragoon?
In Final Fantasy 14 there are base classes and advancement jobs, your base classes include classes such as arcanist, archer, marauder, and lancer just to name a few. Each of these base classes have a job associated with them, with exception to arcanist which has two, summoner and scholar, that require you to level a second base class to 15 to unlock. When you unlock your job you are leveling up your base class since the only thing that says you are your job is the equipable soul you obtain during the job quest. So this means for the oddity that is arcanist leveling up either scholar or summoner also levels up the other job.
Unlocking your job also unlocks more skills specific to your job that your base class will not unlock. By not taking your job when you first can unlock it you're essentially gimping your character since you will not be able to perform your role as well compared to a character with their job, which might be a great hindrance to your party in dungeons and trials and there are many players who get extremely angry over seeing people with no job in dungeons that are level 30+.
Another advantage of having your job is that at level 45 and 50 you get a free set of level 50 class armor specific to your class, so if you are struggling with gear this is a great freebie.
However there is one tiny advantage to going jobless and that is the cross class skills (which may not be a thing anymore come Stormblood). When you are playing as a base class you are able to use any cross class skill on any base class so if you wanted to throw healing skills on a lancer you could if you wanted.
For simplicity I'll ignore the extra jobs introduced after Rouge/Ninja in this explaination of classes and jobs.
The class is what you choose by equipping a weapon. Swords for Gladiators, axes for marauders, Books for Arcanists, etc. These are your basic toolkits up to Lv30.
Jobs are unlocked at you get a class to lv30 (henceforth called the "base class"). This allows a specialisation within that class, along with a reasonable stat boost. You use a job ON TOP of the corresponding base class by equipping the corresponding soul crystal.
It's worth noting that as you level a job, the Exp earned goes to the base class, and the job's level IS the base class'. (you should see text like "Earned X Lancer exp points" while playing as a Dragoon)
The main example for this is the Arcanist, as that class has two jobs: Summoner and Scholar. As the player levels a Summoner, what they are in fact doing is leveling the base Arcanist. The upshot of this is if that same player has gotten to Summoner lv50 (thus the Arcanist beneath it is lv50), then goes and unlocks Scholar, the Scholar will start at lv50 as that's what the Arcanist is.
In short, you don't level the Job, you level the class. And as such gain any abilities from both as you level up as a job. So there's no gain from leveling the class separately, and it will in fact make your job harder without the stat boost the soul crystal provides, as well as the extra job skills/traits and unlocked specialised gear.