A flat foot indicates that you are most likely an overpronater, meaning that your feet roll inward when you walk. You will need to buy a firmer supportive shoe such as a Motion Shoe, to give you maximum control and extra support on the arch side of the foot.
A normal medium arch is the most common foot type. As a normal pronator, this foot type is best suited with a Stability Shoe which provides moderate arch support and good midsole cushioning.
A high arch is the least common foot type. This foot type indicates that you are an underpronater: meaning that your feet roll outwards as you walk. Make sure to pick up a Neutral Cushioning Shoe with a soft midsole to absorb the shock from walking/running.