Personally I'm always lacking for wood. This in turn is because I'm perpetually lacking Fiber. Haven't gotten the Fiber Seeds recipe yet though, so maybe that would turn things around for me. However, as someone who just bought 15,000 wood from Robin less than two months ago in game, the idea of burning up 10 wood for 1 coal is incomprehensible to me. As such, it's Dust Sprite farming for my coal needs, which, using the Burglar Ring and bouncing between elevator floors where they are found, I typically can get around 150 coal (and a bunch of iron) on a day of specifically targeting it.
Your main 3 ways of getting coal can be evaluated like this:
Buying it: Obviously the main thing which determines if this is worth it is A) do you have an excess of money, and B) do you enjoy farming for coal. If A is yes and B is no, buying it is the way to go. In terms of evaluating opportunity cost though, since it costs 250 per starting year 2, for me a day of going for coal gets me around 37,500 in materials (not to mention ancillary supplies of course). If I had an activity which I enjoyed as much or more, which got me things I could sell worth 37,500 or more, it would be better to do that, and just buy the stuff. Or, if I had excess money with no other plan for it, certainly a valid option.
Wood: It costs 10 wood to get a coal in a kiln, plus the setup costs of them, and the interactions to load and unload. If you have an excess of wood with no other plan for it, like literally wood to burn, this is an option. If other options are competing with this for wood, just keep in mind that buying wood after year 2 starts costs 50 per, so it 'costs' effectively 500 worth of wood to get 1 coal, which is double the cost of buying it directly. Of course you can't sell 10 wood and get 250+ in return so it's a bit of an unfair comparison, the point is only that I would only choose this option if I was certain I was not going to be buying wood at any point in the near future, and the wood going in was well and truly 'excess'.
Going for Dust Sprites / Farming it directly: If the answer to A in the buying it section is no, and / or the answer to B is yes, you can always go for the dust sprite route. Alternately, you can get it from rocks, with the Prospector skill equipped. Keep in mind that the "Prospector" skill only affects drop chances from stones to my knowledge, not from enemies. Still, if you have a need of coal, and don't need geodes or have any intent to sell metal bars, it actually makes a pretty big difference in terms of relative ratios of materials found, for what it's worth.