Just gonna throw in some concepts to help the discussion along:
tl;dr - Blue magic is split into two types of abilities: lesser beast abilities and higher beast abilities.Blue Magic
Along with White and Black magic, a third school existed during a time now forgotten. Called Blue Magic, it was an amalgamation of primal forces. Derived from the energy and aether of beasts, practitioners of this lost art at one point could tap into these energies and manifest the fury of beasts in combat.
Two echelons of Blue Magic are known of. The first is the lower echelon, composed of abilities from lesser beasts; still formidable in their own right and relatively easy to put into use, but ineffective in the greater scheme of things. The second echelon is that of the higher beasts. While spells from this echelon place a great burden on the caster, the powers of the greatest beasts to roam the world are a sight to behold.
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Role-wise, caster DPS would be a good place for BLU.
As for learning abilities, an option would be still having spells automatically learned as you level, but not achieving full power until you absorb the essences of the monsters involved (sort of like their own version of a hunting log). For example, at lv15 you'd have the ability Sticky Tongue. When you learn it, it has a 15 second cooldown and higher MP cost, but if you kill 3 toads, you absorb their essence and thus unlock its full potential, turning it into a spell with a 2.5 second cooldown and a reasonable MP cost.
Higher beast skills would be learned via the job quests, and potentially share cooldowns (to keep in line with the higher skills straining the caster in some way).