The Magix site for PhotoStory says that it can import .mov files. If you are not getting sound with videos you may not have the correct option set for importing sound with video. Sorry I don't have PhotoStory but other Magex video editors have this option under either 'Program settings' of 'Movie settings' etc.
Stuttering and choppy playback may be (unfortunately) simply a function of the power of you computer. Many video formats, particularly the high definitions available today, need a lot of 'grunt' to play smoothly and the problems compound when you introduce complex transitions.
Conversion may help for your editing phase, but another option is to live with the less than perfect preview and occasionally check the final result by rendering (exporting) a difficult section on its own. Look for the option to export only a selected range.