1/8 is plenty. I put 2 inch on the last smoker I did, it looks nice, but it's a lot harder to bend than the 1-1/2. Be careful how much welding you do on that, doors warp pretty easily. I just tack my flanges on. I would never use 1/4 for that.
Not a problem on door weight. My pipe pieces are 24" diameter, and what I was told was .330 on the wall. In my research that applies to stainless, but in micrometer terms, I believe its in between 5/16 and 3/8, or one of the other. Either way, weight should be no problem.