Just don't bring this shoes to be used outdoor. Otherwise you can't bring it back into your house for your in house workout. Hehe. Oh yeah, don't forget a pair of comfortable socks too. A shoes complete with socks will be able to absorb the impact of your workout and further prevent any injuries to your feet.
Next is yoga mat. I do yoga once a while but I still use it even when I'm not doing yoga as it acts as a firm grip when I'm doing chess press. I just spread it on the floor and put both my hands on the mat and start pressing my chess to the floor. I no longer have to worry if my hands will slip off the slippery floor. Yay! Oh, I got my mat from Nike. What I really love about it is, it doesn't absorb your sweat. So, you can just simply wipe your sweat off the mat and fold it back after using it. It won't smell. Cool, eh!
Pssst ... if your goal is to burn fat .. FAST, then out of all these stuffs, I'd say you need to shop for your shoes and the speed rope. ;D