The cleanest burning charcoal I can get my hands on for regular use is made from coconut shells, from the same guy who makes my best-of-category ceramic cooker. He ships anywhere, but most affordably if one buys or shares a pallet:
To do better one would have to buy Japanese bincho charcoal, which costs even more. I've used coconut charcoal to bake cherry pies when my oven was out of service; it really burns that clean. For low and slow barbecues I add the smoke I want, by putting wood chips or chunks in a two quart cast iron dutch oven, with holes drilled in the bottom and the lid sealed on with library paste.
For less critical uses I make regular pilgrimages to Lazzari charcoal outside San Francisco, and fill up the car with their hardwood charcoal. They're known for mesquite, but at their distribution center (a disintegrating building with a Mad Max feel to it) they sell many types of charcoal and wood. Eventually I figured out that they use the same hardwood in their briquets as their lump, and a neutral binder I can't taste. I find the briquets burn a whole lot cleaner and more predictably in practice. I can reach 800 F as easily, not that I want to. So why was I part of the obsession over lump charcoal? Something about Kingsford tasting like a petroleum refinery? This isn't true for all briquets, one might consider broadening one's search.
Per la strada incontro un passero che disse "Fratello cane, perche sei cosi triste?"
Ripose il cane: "Ho fame e non ho nulla da mangiare."