Brooks Adrenaline GTS 25
This is the shoe for flat feet — basically the first thing every running store puts overpronators in. I started running about two years ago with the same issue, and the Adrenaline is what the guy at my local shop put me in after watching me walk. It has support built into the sides that keeps your foot from rolling inward, but it doesn't feel stiff or clunky like some stability shoes — just a normal, comfortable shoe that happens to support you. It holds up for gym workouts too (go barefoot for squats).