The deal with a custom stadium is how to shape the materials. I'm trying to figure this out, too.
You can use metal. It just has to be polished to a high shine. The issue is not the wearing of the tips, but how they will take impact with the stadium floor. If you build it out of sheet metal, it can absorb some of this impact, though. To make a stadium from sheet metal, you will require a hammer and a device called an english wheel. Look it up to see what it does. I have seen it used to produce parts for motorcycles.
You may not require the use of an english wheel... You may be able to find another way. It could be easier to find something to use as the "core" of the stadium and then build around that.
Wood. About wood. A wooden stadium will dent when the blades hit it. However, wood may be an excellent base to produce a shape at minimal cost and with hand tools. In fact, I may try this method. Finish a wooden stadium bowl out of wood, and then you can give it a hard epoxy coat similar to those used on garage floors. You can even hammer a thin sheet metal cover for it, if you want to. Or, you can use very thin plastic sheets and a heat gun. Place the plastic sheets on the stadium, then use the heat gun to make them sink into the shape. You can then polish and finish with various sandpapers and polishing wheels/cloths with polishing compound, and you can build the walls out of whatever you like.
Or, you can make a plaster cast of an existing Beystadium and melt the plastic over it. I may take this route.
Currently, I'm experimenting with making an old firebowl into a stadium. I want to give it a high shine and a hard epoxy coat to protect the finish.