Do some reading on here, there are many others in your situation, that are looking at putting their stoves in the basement and wondering if it will heat their homes....Can I comfortably heat my whole house with only a Stove?What size coal stove should I buy? + setup tips/suggestions?
Also, every heating home situation is different. What might work for some, may not for others. Yes, heat will rise, but you may have to get some vents or ductwork to move the heat upstairs better and the cooler air back down.
If you got with a stoker stove, you can put in a direct vent or power vent, then you don't have to build a chimney.
A chimney is a chimney, a stoker or hand fed requirements are the same and it should be installed per your local codes.