The packing process in general should begin about two months out from your move, around the time when you get your moving quote. As you’re going through your home over the last couple of weeks before moving day, you should begin to place items aside in a specific place to be taken in your car.
You should actually start packing your car the day before you’re scheduled to move. Since many of the items you’re taking with you are essential to your day-to-day life, you won’t want to lose access to them for too long.