"Magic should be super-impactful in the right moments" sounds to me like a design dynamic that would best be achieved not through cost or drawback mechanics, but through skill design. Design magic spells so that they are critically powerful but situational (e.g. "deal extreme damage to a knocked-down enemy"; "heal an ally with extreme scaling for their missing health"), and/or add cooldowns to the spells so that the mage can't spam them every turn.
Alternatively, if you want to go for a more traditional MP cost mechanic, and you don't need MP to preserve between battles in your game, you could go for very high MP costs on spells, with "Recharge" skills available for the mages to use when they run out. In timeblazer I only have a Warrior and a Mage - the Warrior uses TP to use his skills (and doesn't have MP), whereas the Mage starts with a full MP bar in each battle and uses a "Mana Synth" skill to convert any TP she's built up so far into MP (which consumes a turn like any other skill does). The upshot is that the mage can hit faster and harder than the warrior, but not as consistently or frequently.
I don't recommend using health as a resource for skill use (except for entire classes whose kits are designed around managing health, like Necromancer or Berserker classes in some games). This is a really cool concept for an anime where the character has to make a choice of "should I sacrifice my well-being for expedience and/or power?", but it's a much less cool concept for a video game RPG battle where the player's actual choice is "will taking the enemy out quicker save me more or less hit points than the cost of this spell?". That choice is easily calculated, and also reduces the size of your target for good battle balance since you are getting rid of incomparables.
