JRT,
I am guessing that you are designing a plane for a heavy lift competition. More than likely, you will be using a conventional configuration, which means that for stability, the horizontal stabilizer will be generating downforce, rather than positive lift. To reduce drag, you should endeavor to get the center of gravity positioned so that the downforce is not excessive, since induced drag from the stabilizer will increase with the amount of lift it generates, whether the lift is up or down. Beyond that, since the hor. stab. will not be generating much lift, it is not a big win for it to have any camber. It will produce less drag if it has a clean, symmetrical airfoil shape, rather than a simple flat plate. If you have time on your hands, and are able to predict the typical downforce you will need and the airspeed, you could choose an airfoil section which produces that lift at that speed at a zero angle of attack, and zero elevator deflection. This would ideally be your lowest drag choice, but since you are already minimizing the lift the stab. needs to generate, it is a small gain. Thinner is better, within reason. Lighter is always better, if it doesn't break.
Good luck,
vortexman