Gas forges fire quicker and you can start working in minutes. Coal takes a lot longer to get a good heat worked up and a lot more maintenance to keep it clean and hot. Downside, building a gas forge can be more costly than a coal. And fuel cost can be a killer.
A lot of gas forges are made with 20# propane bottles lined with ceramic blanket coated with high temp mortar and heat reflective liner. Burners are the big part. You can roll your own to get in the door, but buying one form a place like Hybrid Burners, will be much more efficient.
Coal forges are the old school, tried, true, cheap, and simple way to do it all. Downside, it's filthy, hungry, and a little temperamental. Coal with a lot of impurities can form a lot of clinkers. And, IT'S HOT!!! You WILL burn your metal in a coal fire if you are not careful and get distracted. It's not if, it's when.
A coal forge can me made from things as simple as an old car brake drum and am A/C blower motor attached to a tee on the bottom of the drum with flex pipe.
The local forge group I'm with is on the grounds of a train yard and museum which operates and maintains old steam locomotive, so coal abound. I am building a gas forge for use at the house since there is a 500gal LP tank on the property.
Gas, once dialed in, you can be working with it in less than 5 minutes and is clean. Coal takes a more effort to keep it stable and dirty, but is usually cheaper.
Coal IS more fun to work with (to me at least) because you are more immersed in keeping things rolling. Gas is better if you want to actually work.
E.T.A. Get both. If you stick with it, you are probably going to find some things you need a coal forge for (large pieces that need a truckload of heat) and some for gas (small pieces that you REALLY don't want to burn up...again).