I leveled to 50 Culinarian this past week. All the leve quests are found in the "Drowning Wench" at Limsa.
Here's the items you'll need and the mats associated to make them.
Level 20: Grape Drank = 4 Noble Grapes
Level 25: Chamomile Tea = Chamomile, Water, and something else, maple sugar?
Level 30: Cornmeal = 3 Millioncorn
Level 35: Acorn Cookies = Iron Acorns and a bunch of other sh*t
Level 40: Apple Juice = 6 Mirror Apples
Level 45: La Noscean Toast = Apkulla(sp) egg and a bunch of other sh*t.
You'll also need a gazillion fire and water shards to make those items. It's best to have a BTN or MIN class level to at least 20 so you have the bonus when farming for crystals. If you have a high level BTN, then farming for the mats should be no problem for you, otherwise expect to pay a premium for the required mats. If you're rich and/or feeling lazy, you can always buy all the items from the market.
Of course, HQ items provide a 200% turn in. I don't remember how many mats/items I needed to level every 5 levels or how much exp I got from each turn in. But I do remember doing the level 45 leve and turning in 9 HQ toasts for 351,7xx exp points just on 1 leve!!