It's funny--you could be forgiven for combing through a decent pile of medieval scholarship and getting the impression that everyone wore wool all the time with a supplemental aristocratic desire for "exotic" silks. Candle wicks, on the other hand, are practically a "Who's Who" for all the other textile materials!

For most of the Middle Ages, the go-to wick yarn in western Europe seems to have been linen (flax). Although you can sort of talk about areas of more intensive flax cultivation, for example around southern Germany and Switzerland, the crop was pretty much ubiquitous and so locally available. The other common fiber--both in terms of universal cultivation and in terms of actual use in candle wicks--was hemp. It's notable that in parish records of donations, "yarn" is usually all you get rather than the particular fiber, suggesting that in terms of use there wasn't a lot of difference between the two.

Where we do see a sense of superiority of material developing, on the other hand, comes with the introduction of cotton to Europe. Although I, at least, usually associate cotton in the West with the Canary Islands plantations in the fifteenth century and then of course New World colonization, the fiber actually entered Europe from the Near East around 1200! It wouldn't be used for clothing textiles for longer, apparently. But it quickly became a popular material for candle wicks from Italy to Germany to England.