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Unfortunately I am not experienced much in the art of crafting, however I can make some insightful suggestions from what I have heard and seen from more experienced crafter friends. My primary suggestion is to choose a craft that would benefit what you play the most. For example, one with Ninja as their most primary job should consider woodworking or alchemy to make their own stockpile of ninja tools with minimal costs. Alchemy would benefit a Corsair in the crafting of bullets, woodworking for ranger's arrows, and so on.

Putting that aside another way of looking at it is if your craft is primarily to make money, do you want to do it in the fashion of making high demand gear with a possibility of HQ for big ticket profits, or create constant demand consumables that fly off the shelves but at a lower but faster paced price.

Alchemy is a decent mix between the two since it creates various weapons, armor and consumables as well. Crafts like Smithing, Goldsmithing, Bonecraft and Leathercraft are more gear (thus HQ) dependent while crafts like Cooking, Woodworking, Fishing and Alchemy are more consumable based.

Any craft can yield good gil if you closely watch the market. How you want to make it is up to you. Hope this helped.