Very nice stick burner smoker! I like the whole setup including the roof overhead. This is a good buy for 500 bucks, I think you will get a million bucks of fun out of it, ha ha. Interesting lid lift mechanism, looks like a bottom plow lever.
Beech is used for food crates/boxes because it is basicly oderless and flavorless- will not transfer a wood taste to foods. I would think beech would be ok for stick burning, I'd give it a try and see. You could always mix in hickory or apple for a traditional smoke flavor.
Best of luck and have fun!
The Renaissance Man.