That's a single speed. You need both brakes. If, for some reason, you only wanted one brake it should be the front one. Not the rear.

Since it's a single speed converting to fixed gear may be as simple as removing the freewheel, flipping the wheel around and installing a cog and lockring. What kind of hub does it have in the rear? Does the side that doesn't have the freewheel on it have threads?