Culinarian is a crafting class, which supplies other classes with a different meals that can increase the stats relevant to them. This class requires a large assortment of ingredients, and this fact may make you need some external storage for your items.
Culinarian's Guild is located in Limsa Lomnisa like the Fisher's Guild, and you are able to start fishing and cooking as soon as you complete the Lv 10 Main Scenario Quest.
After you join the Culinarian's Guild and obtain your first tools, you are free to do what you like, but it is useful to complete some additional beginner quests to obtain more crystals for further crafting. All low level ingredients, may be purchased from the guild receptionist and in the nearest market. They can also be found as drops from creatures nearby Limsa Lominsa, or as the products of other crafting and gathering skills.
One thing, you may troubled with, is a journey to Botanist guild in Gridania. TODO: see, what ingredients are needed till 20th level and what of them may be found in La Noscea.
The guild will provide you with all necessary tools and equipment while you completing guild quests. Also, guild quests are the shortest way to obtain crystals.