I (almost) always gralloch my deer in the field as I understand doing it is best for the meat.

If I do it at the garage, I do it head down. I saw the hip bone and the sternum and everything comes out easy peasy with the help of gravity, falling directly into a rubber bucket and without much messing.

Whichever way I do it, I leave it hanging until rigor mortis disppear, when I skin it and debone it.