In general, the earlier the better. Do not postpone reserving your movers until the last day. This will lead you to more stress as you will find out that most reliable moving companies will be booked way in advance.
We recommend that you book your movers at least 2 weeks prior to your move day. The main reason why people delay reserving a moving company – is the price. The delay will never decrease the cost, in contrary, it will only increase it.