Once you have passed a Level II inspection then had the stove installed to the listed instructions and building code, permitted and inspected if required locally, notified your insurance carrier and read the operating instructions then you can consider heat management. Yes, using the existing forced air ventilation is an excellent economical means of heat distribution. I call it "spreading the joy" around the house. Fans are cheap to run. By using your existing ductwork, you remove the excess heated air from the room with the stove, ventilate the house, filter the air, mix the warm with with the cooler stale return air and in so doing, equilibrate the heat throughout the house. It makes the house more comfortable while saving a little energy.
hire a pro to inspect your fireplace first then, once repairs have been made, you can begin shopping for stoves he advises might be suitable for your application. Note: if you have a factory built fireplace, you cannot install a woodstove insert into it no matter what the mfr. says. It is a fire hazard.
HTH,