I am probably not the best person to ask since I have a gas grill but I'll tell you what I do with my fathers BBQ pit and it may give you some ideas.
He has a brick BBQ pit with two grills.. one is simply a whole in the brick wall with a grate at the top.. Its like a brick square with a grate to hold food over the fire and cook directly over the flame... (It has a cast Iron door to control the flame and the top of the fire is completly exposed from the grate. The second area is the same brick over with cast Iron door but has a brick wall with vents and the grill area is also enclosed in an oven.... The vents allow smoke and heat to rise in the above oven to smoke/sorta indirect grill.
To build a fire over the 1st grill I simply do it like a normal fire, I think this could work with an offset smoker or something but again I dont have experience in that area. I normally use logs for larger cuts but for burgers, steaks ect. I use chunkcs and just put some newspaper on the bottom a few chuncks of wood on top of the paper and some wood kindling and let her go and add fire as needed... I would think this would be the easiest since would burns fairly easily and consistently unlike piles of charcoal which need the chimney.... again I dont know your set up and havent used anything like it almost for sure...