FWIW, "smelting" means "to purify or convert ore into metal". When it's already metal, you're just recycling / melting it.
Induction isn't terribly hard to do, but to build anything more than a few hundred watt toy requires serious parts and engineering. I think John's working on the most likely candidate, as far as power * availability;
http://www.johndearmond.com/2014/11/01/using-the-induction-heater-aluminum-casting/To really melt much of anything, you're looking at 3kW minimum; I'd say 10kW is where it really starts. Needless to say, you need enough electrical power available to begin with.
The capital cost of an induction furnace is usually too much for the amateur to justify, at least for low-melting nonferrous metals (aluminum and bronze). Even with lots of hand made parts and discounting your labor to $0.00, you're looking at maybe $1000 of parts and equipment and months of work. It's a great project, for projects' sake, but not so great for the foundryman.
If you're planning on doing a lot of cast iron and steel, the speed and efficiency gain may be worthwhile -- you might be looking at maybe $0.50 of electricity to do a few pounds of metal, whereas it might take hours and a pile of fuel to do it otherwise; and that's if you can achieve the temperature at all.
As for fuels, back in the day when I was playing with this stuff -- I recall hardwood working surprisingly well. Briquette charcoal is crap, don't use it (it's ~20% slag, anyway). Lump charcoal is good, but don't buy it in any less than bulk; or make it yourself. Coal is good too, but hard to find by anything less than the traincar (local blacksmiths or groups may have some leads, though!).
If you're having problems with cinders, I'd suggest a nice hat, leather coat, and maybe gloves (good for protecting the hand surfaces, but, the cuffs trap cinders, too!). Besides looking stylish,
you'll save a lot of money over most of these options.
Tim