Green Mage/Green Magic originates from the Ivalice entries (FFXII, FF Tactics & spin-offs) and essentially is built around buffing allies (Protect, Shell, Bravery, Faith) and debuffing enemies (Blind, Silence, Sleep and Poison usually).

It technically makes more sense as a dedicated Healer job, however a support-oriented Caster (more-so than Red Mage) with both offensive and defensive effects could be created, with using damage built around status effects (DOT application, ripping DOTs out for spike damage, delayed damage although that's more of a Time Mage thing).

Regardless if Healer or Caster, Green Mage would definitely be a favourite of mine as a job hailing from the Ivalice series.

Note: Green Mages in various entries wield Hammers & Maces. *happy combat cleric noises*