You only need basic equipment for each sport to get started.
Swimming
A swimming hat is a good idea to help you go faster and goggles will help you see where you're going!.
Summer is officially the triathlon season but even so, a full-length wetsuit is a good idea if swimming outdoors!
Cycling
A bike is essential but it can be any kind as long as it is in good condition. All triathletes wear a helmet.
Your shoes need to be easy to get on and off during transitions. Cycling shoes that attach to the pedals are an advantage, but not essential.
Running
A good fitting pair of trainers are the most important part of the run and you should wear something that is loose and comfortable.