DRG = Strict combo rotation and some positionals. Jump every 30 sec. Party dps buff.
NIN = Different length combos and lots of buffs and debuffs. Ninjutsu every 20 sec. Party support.
MNK = The most positionals and a flexible combo system where you have a choice of 2 or more skills for each step of the combo. A stacking buff that has to be kept up with combos. Suffers most from not being able to hit boss (I think?).
BRD, MCH = Priority rotations based on dot timers and procs. Party support.
BLM = Strict rotation based on timers, procs and mp usage. Suffers most from movement.
SMN = Priority rotation based on dot timers. Gains and uses Aetherflow and Aethertrail Attunement stacks. Pet control is required for optimal dps. Some party utility.
My favourite caster is SMN because of its mobility and easy basic "rotation". You just put dots on, use up Aetherflow to gain Aethertrail and use the correct filler cast in between. It's really easy to manage while dodging and allows you to focus on the fight. The most annoying parts are controlling the pet, swapping to adds if you don't have your instant-dots move available and losing Aethertrail when the boss goes invulnerable.
Out of melees I prefer MNK because of how flexible the combo system is compared to other melee. When boss adds come, you don't have to worry about being in the wrong combo. Swapping between single target and aoe is fluid. Their oGCD moves are straightforward aoes and they have something to do during boss invulnerability periods. The most annoying parts are trying to do positionals when the enemies are moving or their arse is in a puddle of fire, and losing their stacked buff (but unlike SMN it doesn't affect the rotation). You can recover from that fast every 3 minutes with a buff. I'm still leveling MNK but by looking at the skill list I can already tell it's my favourite melee.
If you don't want to level them all to try them out, I recommend at least searching their skill/spell list online and figuring out how the rotation works at level cap. Then discard the classes that have a mechanic you find really annoying and try out the rest.