Most players can playback most disc types but there will always be brands of media that cause issues for some players.
The main thing for you to concentrate on when buying a player is to get one that [I]supports[I] region free (you noted zones in your initial post). Aside from that, always use a quality media and you won’t have playback issues.
The Oppo players have excellent PAL to NTSC conversion, support region free, and have excellent video quality. If they are out of your price range, you could settle for a player such as the Philips 5982.