Personally I would recommend DVD players made by Sony. They have a good reputation for reliability and good build quality. Additionally, they generally offer a good warranty which should cover you if anything does go wrong. They are not the least expensive players, but they are generally durable and will last longer than cheaper machines
Samsung is the best company for DVD machines. They deliver great video and audio performance as well as compatibility. The on-screen interface of the Samsung DVD machines is attractive, with full-color graphics and animated transitions between menu options. I recommend Samsung because it is a very responsible and innovative company.