Some people cut lino blocks for printing, but I remember cutting lino blocks in high school art class and thought it was tough material to cut, resulting in a lot of bloody fingers.
My preference is using plumbers gasket material, a rubber sheet that can be found in a hardware store. It comes in sheets up to 12" square. It is easy to mark a design on the rubber. It can be cut to your desired shape and size with scissors. It carves very easily with a linoleum cutter (no bleeding!)
After I have my design cut, I mount it to a flat block of wood using water resistant double sided carpet tape - also found at the hardware store. This keeps the stamp surface flat for a good print, and because it is water resistant - it holds up well to multiple washings.
The resulting block is very easy to use. I like to pour several colors of paint onto my palette (a disposable foam plate) and use a foam paintbrush to daub the paint on the block. With this technique, I am able to achieve a nice variety of shades and colors with each printing. For best results, use a padded surface for printing on fabric.
I usually stamp with a variety of acrylic and fabric paints including my favorite - Jacquard Lumiere metallics. Clean up is easy with soap and water and an old toothbrush.