Ranged Phys classes would probably be good. Red Mage probably isn't a bad choice either.

Phys melee classes tend to have a wind up period, which can make them annoying to use on trash mobs. Dragoon has a faster wind up, but you still gotta keep blood of the dragon up which can be tedious running from mob to mob, though not as annoying as Monk or Samurai.

Btw, if you need monster parts, I highly recommend leveling a combat retainer if you haven't already. It doesn't replace immediate harvesting if you are trying to craft something right this moment, but it's a good supplement supply.