Fire works

Fuel-wise, that is. If all you're needing heat for is hardening/tempering, there are some very nice electric furnaces out there for the purpose, but if you're planning on forging, you're looking at one of three fuels: gas, coal, and charcoal.

Gas
Natural or LPG. You can buy a gas-fired forge, or there are a lot of plans out there to build one. It costs about the same as running a coal forge from what I'm told. It burns clean(very nice in any case, especially if you're in a city), it's fairly easy to set a heat and keep it there, anywhere from low forging heat to welding. The one real problem with it is that once it's lit, you have to keep it going; you can't turn off the blower for a while and then pump the fire back up later, it's either on or off. You can turn it down, but that's it.

Coal
Probably the most used fuel. It's plentiful, it's Traditional, and it works. Once the fire is going you can keep the draft going a long time, just pushing fresh coal in from the edges of the fire; if you turn the blower off, the fire dies down but will take a long time to go out. Increase the air blast and you get more heat, reduce it and it cools down. You can make a forge that has a relatively small fire for most work, and there are ways to add in a different air grate to make a much wider or longer, more narrow fire.

Coal definately has drawbacks. You need to get good low-sulphur coal both for reducing smoke and because sulpur in a fire where you work steel is bad. You need to break it up to small pieces before adding it in. And it's dirty(spend a while breaking up/shoveling/whatever coal and see what your hands and arms look like).

Charcoal
Probably the earliest fuel, and definately the most favored for many centuries. It burns fairly clean(little smoke, no sulphur), and will do anything a fire with coal can.

Drawbacks to charcoal are two: cost and availability. You can use commercial charcoal briquets, but it's a mess; the binder they use to hold the powdered charcoal in that nice shape causes the fire to produce a lot of ash, and it clogs up the fire grate. And it can blow out of the fire like a pyroclastic flow in miniature when you bump up the blast. Raw charcoal works very nicely, but finding it in quantity- which is also the only way to get it at a decent price- is not easy. And it takes more charcoal to get the same amount of heat as a given amount of coal.

Let me deal with one other thing here. It's kind of folklore that working steel in a charcoal fire will make it better. Not true. This came from people thinking that 'charcoal is carbon, and carbon added to steel is good, so a charcoal fire will add carbon to the steel'. But it doesn't work that way.

When you heat steel to the critical temperature, that needed for forging medium and high-carbon stuff, the crystilline structure changes, it 'opens up' and the carbon atoms that were locked in the matrix can move around. Not only inside the metal, but those on the surface, and moving to the surface, combine with oxygen in the air and go away*. Which means that every heat you do, you lose carbon from the surface. It's also a factor in scale formation, which causes you to actually lose metal from the bar with every heat.

You can reduce this in a couple of ways. One is to keep the fire going so that the area where you actually place the steel has a 'reducing' atmosphere, i.e. most of the oxygen burned out(though you still lose a bit when you pull it out to hammer/punch/twist/whatever). The other is to use something to coat the steel. This is one of the things flux does when used in welding: it both lowers the melting temperature of scale or other impurities that may have gotten between layers to it'll melt and be forced out when you set the weld, and it coats the surface and keeps oxygen off. It works, but it's not really practical for general use.

So, back to the main subject. I've used coal(still do) and charcoal. If I could find charcoal at a good price I'd use a lot more of it, especially for hardening blades. I haven't used a gas forge, so I have to go by reports from people I know and what I've read, which are enough to make me want to build one in the future if I can keep doing enough forging to make it worth it.

So take your pick, they all work, and find the one you like.

*Case-hardening does often use charcoal as one element in a sealed atmosphere to increase the carbon content of steel. 'Sealed atmosphere' being the key, because you have to have the metal surrounded by the carbon-bearing material and sealed away from the air. In the old days that generally meant inside a clay crucible or chest with a lid sealed on. Although for small pieces you can wrap them with thin pieces of leather, maybe put some other stuff on or in the wrap, then coat it with clay to seal it. Then the whole thing is placed in a fire or furnace and brought up to heat and kept it there a while. There's enough carbon around the steel or iron that some migrates into the surface, I seem to remember reading either 1/64 or 1/32" per hour. You can keep it going long enough to convert a bar of iron to steel all the way through, though if you're not careful it tends to be of uneven quality from end to end(which is one reason laminated or pattern-welded steel was developed).