I used 0.8mm stainless steel for my nimblewill stove.
Cutting stainless is a right swine - it was one of those jobs I wished I hadn't started, but was really pleased I had once completed. The nimblewill stove is not only one of the best pieces of kit I have, it is made even better by the fact that I made it myself. I made mine slightly wider than the plans provided.
Cutting mild steel is easier, but it will rust quickly, especially after firing. Stainless won't.
I got a good sized sheet of stainless steel from a local sheet metal worker - it was an off cut and they let me have it for nothing.
If you don't have the tools for cutting stainless then you will have to buy them, at which point it may be just as cheap and easy to buy a Honey Stove.
Anyway, the simple answer to your question is to use thin (0.6-0.8mm) stainless steel. Don't be tempted to use mild steel - you'll regret it in the long term.
hey mate, i would avoid ali as it tends to warp, stainless or titanium is the prefered choice for most wood or multi fuel stoves, it is a git to cut but worth it, as for thicness, depends on what kind of use it will have, for a square wood burner i would go for 1mm, as an average, no lower than 0.7 because of warping, no higher than 1.5mm because of weight. hope that helps, i operate a water cutter for the engineering industry and have made a couple of flat pack fire boxes in the past