First, where will you do the most of your training? On the road/treadmill or trails? Road running shoes are designed for the repetitive strides of road running, where your feet will be hitting hard and, for the most part, even surfaces. Trail running shoes are designed for varying and unstable terrain. They are heavier than road running shoes, due to their thicker sole, which protects your feet from underfoot dangers like sticks and rocks, while also providing stability.
What kind of feet do you have? First start with the length of your foot. Do not be afraid to ask someone at the shoe shop to measure your feet. Then, check the width of your foot. If you are a male with a more narrow foot and cannot find a shoe in the "Men's" aisle, try a pair of "Women's" shoes, the same goes for women with wider feet, try the "Men's" aisle. Most shoe manufacturers design their women's lines with a B width and men's lines with a D-width and not all feet are created equal. Next is your arch! Think about what type of footprint you leave in the sand. Is your footprint narrow and curved? You have a high arch. Does your foot leave an almost straight print? If so, you are flat footed. A great way to check is with wet footprints on concrete. Here are examples of what you are looking for: