Good question, Elk!
Good quality chunk wood is essential (no offense to chips or pellets, I'm just a chunk guy)! Aside from the hickory dowels that came with your smoker (which, btw, impart a very good hickory flavor), I get my wood from Fruitawood.com or MaineGrillingWoods.com. They offer very clean, properly-seasoned wood designed for smoking. I've never been disappointed with the quality or selection.
To me, the best thing about these smokers is that you can focus on the prep of the meat (seasonings, rubs, brines, etc...) and the type of wood smoke flavor profile you are looking for - not the process of actually cooking! Because these smokers are so tight, and hold moisture so well, we can use much less wood than many others smokers use. That also means the only thing that affects the flavor of the meat is the prep, and what kind of wood you use! There are very distinct differences in the hardwoods and fruit woods that we use, but you need to experiment with that yourself.
Wood smoke flavor is very subjective, but there are some guidelines available for what wood to use. Everyone is different on how smokey they like things, and what flavor of smoke. For example, I can use hickory on just about anything. I grew up in Arkansas, and it's the BBQ wood of choice down here. But, I absolutely love cherry on pork and poultry! It's a different flavor, and a little milder than hickory. Big mesquite fan for beef, as well as oak and hickory. But, that's just me!
I find the wood smoke flavor to be much more "true" in these smokers than any other way I've smoked BBQ. There is no influence on it, except heat!