After you choose a moving company and pin point the move-in date, make sure you ask what the start time is. You want your start time to be first thing in the morning, to allow you added time for unexpected situations. If your start time is any later in the day, most likely you are scheduled after another move.
If your move is not scheduled to be the moving companies first move of the day, you risk having to wait around for your movers to arrive and even have your move run overtime into the next day.
Moving is usually stressful enough, make sure your move is scheduled for early morning and will be completed that day, if it is a local move.