I believe that EMI could stand alone as it's own game. It doesn't need the other three games to be played first to be fun. But I would recommend playing all of them since I don't think there are any "weak" games in the series, as long as you can put up with some outdated graphics. Besides, a lot of EMI is based on earlier happenings in the series, but their not that important, so they can be overlooked.
All 4 games AND Grim Fandango is my advice.
If only we had as much graphic adventure games as Star Wars Games!!