Technically you want to avoid anything that weave (and espcially double)

I'm no Monk expert so I can say for this job but I support the above claim that Samuraï is a good idea.

BLM has little weave BUT you might have a hard time knowing if you can finish your cast or not.

I wouldn't advice DRG at all. Not only because of the weaving but also because of the animation lock (added with the alg it might be nasty)

Ninja / SMN and MCH are no go imo.

So I'd say
Melee : Sam (monk maybe i'm not sure)
Range : RDM (eventually BLM if you don't do Savage)