Hi Steve, welcome to the forum.
Since you currently have a wood stove, are you 'ok' with loading a stove twice a day? If so, a hand fed stove will do fine. If you choose one of the ones with a gravity feed hopper, it will stretch the time between adding coal to the stove, but it will not change the need to at least look at the stove twice a day, and shake the grates a bit to get the ash to drop, so the fire will continue to burn well, without ash blocking the airflow.
If you think you'd like to free yourself from tending a stove every 12 hours or so, you can go with one of the many stoker stoves, most will go a full 24 hours and many double that on one hopper full of coal. The ashpan might require emptying more often than adding coal.
If you don't need the look or radiant heat from a stove in the basement, but just want to heat the house, there are several stoker hot-air furnaces available, Leisure Line has a nice small one, and there are many others that are meant to be a FURNACE for the house, not a room heater like a stove [either wood or coal].
Probably the 'Cadilac' version of using coal is to put in a boiler, use a water-to-air heat exchanger in your furnace ductwork plenum, this will heat your house just like the gas furnace does. But the bonus is that a boiler will also provide all the domestic hot water for your home. Most boilers can provide virtually unlimited hot water.. Do you like 2 hour long hot showers ??
Some hot-air furnaces can be equipped with a hot water 'loop' but they are low capacity water heaters, and are meant to add heat to your existing hot water tank/heater. Which type of hot water heater is best depends on the size of your family, or number of people using hot water each day,, and also if you use a 'loop' to heat the water heater tank, is WHEN the hot water is used.. if all a once, showers, laundry, dishwashing etc, the loop will not help much, but if the use is spread out over the day, then the loop can do a lot.
Let us know how big the house is, level of insulation, quality of windows. All this is to try to determine the size and type of coal burning appliance would work well for your situation.