To get the most out of your Barre on the Ball class, it's important that you have the right size ball. This is determined by your height, but every Swiss ball manufacturer has slightly different size charts, so make sure you check the size chart of the brand you are going to order.
My personal recommendation is Trideer brand. They cost a little more than some others, but they hold their shape well and do not stretch as quickly as some of the cheaper ones on the market.
The crucial test of your ball is when you sit comfortable on it, your thigh should be parallel to the floor. For most of the exercises we do in Barre on the Ball, I would say if you are in doubt, order a size down.