Move steps that should be executed during the final weeks before the move.
Call utilities in your current state and set your shut down dates for your electric, gas, sewer, water, trash, telephone, internet, cable/TV, and any other service you currently utilize.
Get a letter of reference from each utility company. This will help you avoid deposit fees from the new utility companies, many companies have an option for this letter to be ordered on their websites.
Call utilities in NH and set up your start dates and appointments for installations.