I always grill over wood or charcoal fire. I will add mesquite or hickory wood to the charcoal fire to create smoke and put the lid on the grill when the meat is cooking.
Chicken I marinate with Jamaican allspice, garlic powder (not garlic salt), mild paprika, hot pepper sauce (like Tabasco, but less expensive), and soy sauce. Mesquite chips burning and producing smoke is mandatory.
For pork I just use ground chipotle pepper. I buy pork very red so that as soon as the red is cooked out it is done.
I cook indirectly with the charcoal in one corner of the grill and the meat in the opposite corner. BBQ sauce is added only when the dish is served, Kansas City style. I normally use Pickapeppa Jamaican style sauce, & Christa uses Kraft Honey BBQ sauce. I buy the family pack and make a project out of cooking so there will be cold leftovers during the week, especially cold pork.