In general, shopping at WT Kirkman for wicks is a good place to start. The wicks he sells generally work well.

You will occasionally run into a lamp/lantern that prefers a wick with some special characteristic however. For instance, I found that #39 style lamp burners prefer wicks that are on the thicker side. Even the wicks sold by Adlake for their newly made #39 burners don't seem to work all that well, as they are a bit too thin. I wound up buying wicks for that style burner from a half dozen places and found a couple sources of thicker ones that seem to work much better than the thinner ones. I had a couple of people send me some old "original" wicks that they found in old #39 lanterns, and they amazingly enough all measured on the thick side too.

So, there may be a tiny bit of trial and error in order. Most of the time it doesn't seem to matter, but if a particular wick does not seem to like a particular lantern, don't be afraid to experiment.

A tip... I usually throw a new wick into the microwave oven for 15 seconds or so to help remove moisture that they seem to accumulate out of the air while in storage. Sometimes I have to repeat it a few times until it feels dry. Don't go to long in any one trip into the microwave though, as they will burn if left in there too long.