The present invention is a cooking grill having as its cooking fuel source charcoal, wood, or similar solid fuels and comprised of devices for acceleration of ignition and temperature elevation of the solid fuels so as to lessen cooking preparation time and increase cooking efficiency of said grill. The invention is directed to a barbecue unit capable of accelerated ignition and burn time of charcoal, wood chip, or similar fuel. The unit is comprised of an accelerated ignition system having an ignition box, heating element, plurality of transportable fuel baskets, basket transfer tool, high-pressure forced air supply device, automatic sequenced timer, and ignition air diverter. The unit is further comprised of supporting racks affixed to the shell of the unit and operable to hold the transportable fuel baskets in a plurality of configurations such that heat can be applied directly or indirectly in the cooking of the food. In addition, the barbecue unit of the present invention is comprised of a waste removal system for clean up of the unit after cooking, said waste removal system being capable of processing and disposing of ash, grease, food, and other waste remaining in the unit after the cooking.