Production Skill -> Harvestable Family

Alchemy -> ore and herbs
Armor crafting -> ore and herbs
Blacksmithing -> ore and wood
Carpentry -> ore and wood
Cooking -> wood and herbs
Tailoring -> wood and herbs

Alchemy and cooking are two Asda Story Gold exceptions. While they require materials from two of the harvesting families, they also need supplies from a vendor on all of their recipes. Alchemy uses vials and containers. Cooking uses additional types of food including fish and frog legs among other things. All of these are found at an alchemy or cooking vendor. These vendors are usually next to the crafting tables.