Recycled bricks are free! If you know where to look...+++1 the way to go
A friend did this with bricks/mortar as a surround/support for his original Weber cast aluminum grill box. Then fitted the grill with new replacement cast iron grills and a propane gas “starter fire ring” underneath a rack made to support the charcoal. Light the charcoal with the gas then turn it off. Excellent slow cooker and smoker. The underside of the “box” had to have a metal slide in bottom which can be removed to remove spent ash. Also easily bored air drafting holes (with sliders for air control from an old wood burning stove) completed the drafting system. Pretty good setup and reuse of the 14 year old worn out Weber.