While Cricut offers plenty of materials just for the Cricut Joy, including Smart Materials which save you a step, you aren't limited to these. You can use a variety of different materials and cut them to fit the Joy. Here are some of the best options.
There are hundreds of different materials you can use with the Cricut Joy. But Cricut makes a number of products specifically for use with the Cricut Joy, including "smart" materials that you can use conveniently without a mat.