I'm confused about how Classes/Attribute points work.

[Enkidoh]

As well, besides having it's base class at 30, there are several other requirements you have to accomplish first as well before you can unlock that class's Job:

Have a certain secondary class at level 15 (which is different for each class you want to unlock a Job for) - for instance, as you know to unlock Black Mage on Thaumaturge, you also have to have Archer (ARC) at level 15.
Completed all the class quests given by the Guild of the class you want to upgrade to a Job (the last one is at level 30)
Have passed a certain point in the main storyline (the level 20 main scenario quest Sylph Management) - this last requirement was a recent change added in the 2.45 patch.

If you satisfy all this, a npc in that class's Guild will then direct you to someone else who will start the Job quest line for that class.

As others have said, a Job is like a modification to a class in that it piggybacks on it and uses it's levels, exp, traits and abilities while boosting your stats in that class and allowing you to use unique abilities to that Job (that you cannot use with any other class or Job). So they are well worth the effort to unlock.

Hopefully that hasn't been too confusing for you.