You want to look for a "stability" or a "motion control" shoe. These shoes can be rather expensive because of a bridge that they put in the arch of the shoe and they also put stabilizers around the heel. I have a low arch and I definitely over pronate. This was causing me foot, ankle, and knee pain when I was starting a walking program. My tendons are very lax and flexible (according to my doctor) so my foot and ankles flop all over the place when I do anything.
I bought a Nike shoe (can't remember the name) that worked really well and was SOOO comfy. I also just bought some Asics Gel Kayano which is one of the top rated stability shoes. It is working well too, but not nearly as comfy as the Nike shoe was. Also, I have heard that New Balance is excellent. My husband uses them; however, I could not find a New Balance shoe that felt good on my foot. But everyone is VERY unique when it comes to shoes. Also, I can't say enough for Fleet Feet. Best type of store to go to.