this is a little more complicated than just use this or that material.. different materials will have different sound absorption coefficients at different frequencies.. for example, carpet may be really good at absorbing high pitched sounds, but terrible with things like loud bass.. just something to keep in mind when looking for the perfect material for your specific scenario..
i have read that egg cartons are quite good, not so much at lower frequencies though, and if you dont mind the fire hazard they pose.. they flame up in an instant, and burn faster than the speed of light, especially when vertical..