A Weber kettle is what I used for years before I got my first offset smoker and then pellet smokers. I used to do the same thing as you; put the charcoal off to one side. I also prefer Royal Oak briquettes to Kingsford any day of the week. I just think they have a cleaner taste
(the Walmart brand is made by Royal Oak and is what I used most often).
Like Smokeasaurus & Tim I MUCH prefer a smaller, hotter fire which burns cleanly.
Wet wood on any fire is DEFINITELY yuck++, because you are creating a dirty burn. I'm also NOT a fan of the minion method. It relies on unlit charcoal and choking off oxygen both of which create an unclean burn, and the food always seems over-smoked to me.
The best things I ever did was to make sure the charcoal was completely lit and ashed over in the chimney BEFORE I added it to the kettle. This is DOUBLY true if you need to add additional briquettes later. Get them lit and ashed over FIRST!
Then I would add just one larger or two smaller DRY chunks of wood (it doesn't take much), OR BETTER YET... make a pellet/chip pouch using a piece of foil and 1/3 - 1/2 cup of wood pellets or DRY chips and punch just one small hole with a toothpick (yes, just one single small hole, THAT"S IT! One... and SMALL!!!). The pouch actually catches any creosote, etc. and releases only clean smoke.
Like this (click the photos to enlarge):
This always gave me plenty of extremely nice clean smoke on my Weber Kettle or my offset smoker.
This method can even be used for cold smoking on a Weber using a few ashed over briquettes and a foil pouch or single chunk of wood, and still give you a great clean smoke. The key is the briquettes MUST be hot and ashed over, plenty of air flow, and the wood MUST be dry!
