Leveling crafting by buying all the turn-in items for leves and supply missions is faster than making them yourself, but not nearly as satisfying. Personally, I prefer for leveling crafting to involve actually doing some crafting. It just makes more sense that way.

I do use Ixal quests, GC supply missions, and leves to level faster than just grinding the crafting alone would do, but I make the items those leves, missions, or quests ask for. (Well, in the case of the Ixal quests, there's only one of them that allows buying turn-in items. The rest involve crafting quest-specific items that you have to make yourself.)