Even if you’re a strong swimmer a life vest is a good idea in case you’ve injured yourself and can’t swim, or in case of bad weather. Similarly a wet suit is highly advisable as it will help you to maintain a good temperature while you waterskii and if you should go under. This is important for your health and safety but also makes it more pleasant so that you’re not chattering your teeth the whole time and so that you can go barefoot water skiing no matter the time of year.
Finally you might want to invest in some ballast or fat sacks. The purpose of these is to weigh down the boat and to provide extra stability and thereby helping you to balance more easily on your skiis and preventing the rope from waving and shaking and throwing you over.
With these basic items you will then have everything you need to start barefoot waterskiing. As there is no board or skis involved there is nothing else that’s crucial to buy, so that if you rent your boat and rope it’s one of the cheapest and easiest activities to get started with.