Corsets must be made from fabric with no stretch at all. The fabric designed for corset making is called coutil. Although coutil is expensive, not much is needed for a corset. Some cheaper alternatives include canvas, denim and cotton ticking. However, these will stretch over time and are not suitable for any garment with a large waist reduction: they are not strong enough. They are good options for testing the pattern to see how it fits on you. For corsets made from silk and cotton and other fancy fabrics, you need to use several layers - the fabric you want to be seen, on top of a layer of coutil or other strength layer, and perhaps also a third layer made out of lining which will sit next to the body.
For the core fabric, you need a strong fabric, such as coutil, canvas, or denim.
For the outer fabric, you can use most non-stretch fabrics, such as linen, cotton, or silk.