All yoga is good for IBS! And Cyndi Lee's OM Yoga in a Box for beginners is great for beginners with IBS, especially as you can mix the sections...so if you don't want to do standing poses or something, then that's fine.
You don't need to buy anything special when starting yoga. You do need a flooring that you won't slip on easily, which is why a mat is helpful. But a belt does fine as a strap, a cushion as a block and yoga doesn't use balls (that's pilates).
The special clothes are NOT needed. I still don't own any...tho I wish I did. Just wear comfortable clothes that you can stretch easily in.