Lots of good suggestions already. For carpeting you can usually find rolls of old carpet or small pieces of new in the trash area of carpet stores. I use an old shower curtain but there are plenty of $ to $$$$ options such as rubber mats from industrial and restaurant suppliers, attachable garage floor tiles, etc. Home Depot has a good page on a whole bunch of different types of floor coverings to give you some ideas.
Garage Flooring - Flooring - The Home Depot