When selecting an auspicious date for moving, the top two elements to be considered are the Chinese zodiac sign of your family and the orientation of your new house. Generally speaking, the date will be fine if it does not clash your family's zodiac sign or the orientation of your new house.
Water Day rather than Fire Day should be selected. As for hour, Yin Hour should be selected if it is a Yang Day and vice versa.
If your new house is east-facing, do not move on a metal date of Si, You and Chou; if it is west-facing, do not move on a wooden date of Hai, Mou and Wei; if it is south-facing, do not move on a water date of Shen, Zi and Chen and if it is north-facing, do not move on a fire date of Yin, Wu and Xu.