When you’re joining your first Pilates class, you won’t need as much as you think. The Pilates studio will likely have all the equipment that you will be using.
With that being said, some people prefer to bring their own mats, for example, but if you plan to do this be sure that you are using a Pilates mat. These mats are a bit thicker than your typical yoga mat and provide extra padding during your workout. Your Pilates teacher may be able to recommend a good brand.
Remember the studio will have mats that you can make use of before you purchase your own.
Another thing you can bring is your water bottle and a small sweat towel.