... thinking of 20cm deep (front to back) by about 35-40cm wide
You can certainly use mild steel (think of all the tin cans used to make hobo stoves
) but you might not need to.
Many stainless steels aren't hideously expensive. If you're making something as big as that then you might find that it can be almost as cheap to make it from thin stainless as it is to make it from thicker mild steel. You will probably want the steel to be thicker if it isn't stainless to allow for some corrosion.
Do you know any local metal fabricators who work with stainless steels? They will most likely have off cuts that have been cut using a guillotine. They will probably throw them in the scrap bin. Just go and ask. You may also find that the scrap is much better material than you would buy if you were paying good money for it. I've made all sorts of things from 316 scrap from a local fabricator.
Do you have access to a folder? I would think that at the sort of size you're thinking of you would start to suffer from flexing of the sheet metal unless either it is fairly thick or it has some sort of stiffening. You will also notice distortion more with bigger panels. If you can put folds in the metal you can make it much stiffer. Look at the door panels of any motor car for an idea of what I mean. If you can make formers from something like pieces of thick angle and a couple of G-cramps then you can put a fold say 1/4" deep on the edge(s) of the sheet. This will make a sheet of 1mm material nearly as stiff as a piece of 6mm material, but it still only weighs about the same as a piece 1mm thick. Alternatively you can fix stiffening ribs to the sheet, either strips welded on or a piece of angle with bolts.
