Doing leves are the quickest way to level your crafter class, handing in high quality items gives you twice the EXP for faster level up. If you don't mind, let me list up the tradecraft leves with the most fewest/affordable ingredients that you can get to make them. Most of these leves are "Charity" type which lets you submit three times of the same item set with one leves, so it saves your allowance for more EXP per one.

Bold text indicates the leve quest name in English version (not sure about the other languages)

Since you're at level 20 now :
lv20 -> A Grape Idea , you need 3 Noble Grapes per one Grape juice. You can either try to find them cheap at market board or have a botanist friend get them for you. its a lv22 item.
lv25 -> Fever Pitch, I used to spam these back at this level. They need mineral water, honey and chamomile. Mineral can be bought from NPC, honey is often very cheap at market due to people hardly use them for anything. Chamomile should also be either cheap at market or gather with botanist at lv24.
lv30 -> True Grits, you can buy cornmeal at The Whistler Miller in old gridania (near amphitheater) or make the high quality yourself with 3 millioncorns.
lv35 -> Feeding Frenzy, every ingredient (ryeflour/table salt/mineral water) can be bought cheap at npc except the iron acorn, which you either can find them cheaply in market or gather with botanist.
lv40 -> Made by Apple in Coerthas, you need 6 Mirror Apples here. They're either cheap at market or again you gather them.
Alternatively
Moving Up in the World, requires 2 night milk and 1 rolanberry. You need a friend who unlocked the Sahagin Beast Tribe to get you the night milk while rolanberry is either cheap or you gather them yourself.
lv45 -> Red Letter Day Same ingredient as Rolanberry Cheese except the Lassi needs 2 rolanberries.

Hope this walltext guide helps.