Yoga Mat I highly recommend a yoga mat for Pilates that provides some cushion and it does not slide on your surface. AMAZON
36-inch Foam Roller A foam roller is great for massage and release of specific muscles. It also can be used as a prop for stability work. AMAZON
Pilates Clothing & Accesories
Yoga/PIlates socks offer grip traction on the bottom to prevent slipping. Barefoot is another good option. Regular socks will cause you to slip. AMAZON