A healthy body makes a healthy mind. It's important to stay in shape and exercise as much as possible, but it's equally important to keep your feet happy. Playing sports or running long distance puts your feet under far more pressure than daily walking would, so it's essential to support your feet properly. There isn't one pair of shoes that are the best trainers for sport, it largely depends on your personal foot shape, which sports or activities you're engaging in, and the way your walk.
A good place to start is to look at your pronation or foot strike. Most runners will land on the outside of the heel, and transfer weight to the foot as it rolls inwards, providing balance and support to the rest of the body. Some runners may slightly over-pronate while they run, which means the foot rolls inwards more than it should. To counteract this and protect the rest of the foot, you should look for running shoes with extra cushioning. Once you've found a suitable pair to provide support where you need it most, you should think about finding running gear to keep you comfortable (and looking good!).