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"Everyman's Jet Engine" - Why Valveless Pulsejets?
For your first engine, or for any purely "experimental" or "prototype" engine, there is nothing wrong with using plain mild sheet steel of reasonable thickness. Such steel can be successfully formed and welded using even the crudest methods imaginable. The chief disadvantage is that extreme lightness is not possible -- if the steel is very thin, the engine will not be long-lasting.
With any form of stainless steel, strength at running temperature will be much greater, so thickness can be reduced to a minimum. You will also have an engine that will practically "last a lifetime". The main disadvantages of stainless are a relatively much higher material cost and a much higher level of skill in metal working (especially welding). However, most hobbyists who are equipped to work and weld stainless will find building small stainless engines quite easy and affordable, especially if care is taken to minimize waste.