Tim, There are many different ways to fire up offset smokers and each way has its merits and its proponents. I put Royal Oak lump in my basket to about 2/3 full and light it with about 2/3 chimney of Royal Oak briqs. When the lump is fully involved, I put 2 or 3 pre-heated wood splits in and when they are burning nicely I close the CC doors and let the CC get up to temp. When I reach my temp, I put the meat in and add a couple more splits and some chunks of flavor wood. Keep a good, hot bed of coals and always pre-heat your splits.
Season your smoker, and while it's seasoning, play with the size of fire and the air intakes to see how your smoker likes to run. I usually leave everything fully open and keep a small to medium hot fire. My smoker likes to settle in at 260-275*. When it gets to about 255*, I put a couple of pre-heated splits in and prop the door open about 1". At 260*, I close the door. I am really convinced that pre-heating the wood is a key to good fire management. The wood ignites very quickly which keeps the temp from dropping too far and also keeps the smoke very clean.
Give this a try and see how your Brinkman likes it. Good luck, Joe.