Arithmetitian:
Caster with non-elemental, time and space based spells. A utility centric DPS caster that focuses on buffing allies and debuffing enemies, and a rotation based on distance and timing. Visually, I'd would use clear geometric patterns with mathematic formulae.
It would use Rulers or Abaccuses.


Ranger:
Physical Ranged dps, with a crossbow and a Falcon pet. (Wouldn't be a true pet, more like an animation, like SMN egis. But could have some form of interactivity for poses and emotes. )
Would use mechanical traps, nets, caltrops and such, reminiscent of a hunter or a trapper. Would probably be a selfish dps, like machinist.