Historically tests such as the 'wet foot test' have been recommended to identify your foot type and therefore pick the most appropriate class of running shoe in order to minimise injury. Whilst this is still widely used as a guide, several pieces of recent research have suggested that choosing a class of running shoe based on foot shape/arch height alone has little influence on injury risk. However as this seems to be rigidly set within running community doctrine it is something which sadly may habitually live on for some time, purely for its ease. See here for a more in depth discussion regarding this research.
When deciding which road running shoes are best for you several factors must be taken into account, not just foot shape or foot position alone. For this reason it is often best to see a Podiatrist if unsure or if buying your first pair of running shoes.
The general consensus with regard to how often running shoes should be replaced is between 250-500 miles (depending on factors such as body weight/running style etc).