My preference is coal. Easy to change the shape of the fire as needed. Easy to ramp the heat up or down as needed.

No billowing clouds of "forge-fleas" as with charcoal. No big 'ol heavy tanks to lug around. (Just big 'ol heavy sacks!)

I use a muffle for heat-treating.

Depends on your purpose: Propane is the best for most purposes, you get a more even heat, less scaling, however both the forge and the fuel is not cheap, and welding could ruin the insulation. Coal is good: it gets hotter than charcoal and uses less fuel, forges are easy enough to make and cheap to buy, but It can be dirty with uneven heats that can cause warping in the blade and scaling, not good for heat treating a blade. I use charcoal because everything about it is cheap and easy: my forge cost me about 10 dollars and the charcoal itself I can pick up at the grocery store. Just remember natural lump not briquettes.

At the end of the day, it's the skill of the cutler rather than the tools and fuel that make for a quality piece. A cutler who knows the properties of her/his fuel can do just as well, even if that fuel is seen as inferior by others.

That said, I use coal because I only have a coal forge at the moment. The benefit of coal is also its flaw: high, quick heat. Using coal, one runs the risk of raising only the outside of a piece to heat, leaving a realtively hard and cool core. When worked, you end up moving the hot sheath of metal over a stationary core, causing internal stress fractures. (This is particularly true if you are working thick material) Always give your piece a good soak in a coal forge, and make sure it's free of clinkers. The scaling issue can be largely remedied with Borax.

Propane is a good heat source, but it's expensive and potentially more dangerous than coal. It also requires more equipment and machine parts. Propane gives a more even heat, and it's thus more likely to soak through. You don't have to wait for propane to coke up, and you don't need to maintain a reduction zone within the dome of fuel.

I suppose the costs/benefits are different for everyone.

If I were making knives often, I would probably go with propane mostly for ease-of-use. For general blacksmithing applications, I prefer coal. But let's not forget the handy acetylene torch for hardening and tempering.

Charcoal freak. No sulfides to make the steel brittle, no limited heats before carbon migration get to be a problem. Manual air blast will generate enough heat to really mess of everything up to 52100. Can selectivel temper right in the forge. Build a simple air forge in an expired gas rill body and the neighbors think you are bbq-ing

Oh, needs to be said..... best way to cook a pepper encructed filet to Black&Blue is over a realy hot charcoal fire.