Shin splints can be a nasty and painful injury to deal with, and unfortunately are quite common among runners. Shin splints are defined as intense pain that runs down the front of the shin, and occur typically from overuse, running too much, or running repeatedly on hard surfaces. Too much repeated pounding on roads and other similar surfaces leads to swelling of the muscle on the front of the shin. This inflammation, which then pushes into the tibia bone that runs down the front of the leg, is the painful sensation known as shin splints.
Because this is an overuse injury or an injury caused by increased stress and weight on the shin, the best shoes to buy will have plenty of cushioning, bounce, and support in the insole. They will have thick insoles that help absorb the shock that is generated during your run, and provide comfort for the shin muscles so they do not swell and become inflamed. Therefore, the best shoes to look into purchasing in order to prevent shin splints (or to keep them from worsening) are thicker shoes with a lot of cushioning and support.
Brooks Ravenna, Launch, and Ghost shoes are great options. They are sturdy and well built, with a lot of cushioning in the insoles. They work extremely well to absorb the shock and stress from repeated pounding. Asics also make some great shoe options for shin splints, including the Gel Nimbus model which features a super comfortable and shock absorbing gel insert. Saucony's Triumph ISO 3 and Zealot ISO 3 have recently increased in popularity among runners because of all their features. Not only are they great for helping you avoid shin splints because of their thick cushioning and ample support, but they are designed with a cushioned top sole to further help absorb running impact, and create more bounce in your foot strike (which not only helps with shin splints, plantar fasciitis and other common running injuries, but it even helps make you a bit faster by adding additional bounce in your step).