Don't shave, you'll end up with a bristle-y moustache! I just buy these little lip wax strips that you warm up between your hands, stick on the 'problem area' and tear off! Works a treat. My 'tache is barely visible anymore :)
Olay makes a two step moisturizer and hair remover. If you can afford laser hair removal or the no no machine they will permanently or almost permanently get rid of it. Do not shave! It will come in darker and thicker.