Disclaimer--I'm an overbuilder and like to do things right (that is a relative term) the first time so I don't have to fix it after a couple of years.
Would 1/4" steel plate make a good firebox? Sure it would. Want to step it up a bit? Use 1/4" stainless steel instead. It won't crystallize and flake (over time, when subject to heat) like regular hot rolled steel plate, which will give it a longer life. I'm sure people have gotten many years out of 1/4" steel fireboxes though--I'll let others attest to that.
As for insulation, I've had good results with mineral wool that I purchased from McMaster Carr. It's reasonably priced and as I recall, you can get it in various thicknesses. I used 1 1/2" square tubing as my frame for my cooker, so 1 1/2" thick insulation was an easy call for me. I don't know if you plan to frame your firebox out first,but if you do, keep in mind that the frame will transfer heat out to the outer skin. It won't get red hot, but it'll be too hot for comfort. Mine gets hot enough that it hasn't flaked the paint, but I won't put my hand on it.
For the outer skin, I'd think that you could go as thin as 14 gauge as long as you broke X's across the pieces. That will give it some stability and keep it from warping when welding. Keep in mind that you can add some serious weight for no reason when putting on outer skins.