Foreign Service employees are issued Diplomatic Passports at no charge. They are issued prior to the first overseas assignment. There is no special pricing for personal passports. You do not need to obtain a personal passport before orientation.
You do not need to get a personal passport before orientation, but you probably will want to get one before you leave for your overseas assignment. Diplomatic passports are for work use only, meaning that if you take a personal vacation somewhere, you would probably need to use a personal passport. The rules around the use of a diplomatic passport when you are overseas are complicated and best explained by your RSO and/or consular section, but you'll want personal passports in addition to the diplomatic passports.
U.S. citizen eligible family members on your orders will get diplomatic passports, noting that they are dependent on diplomat on whose orders they are. Members of Household, such as an unmarried partner, parents of the diplomat, etc. will not get diplomatic passports and will travel on personal passport. If your spouse is not a U.S. citizen, he/she would travel on a personal passport from whichever country he/she holds citizenship, but may get a diplomatic visa to extend the same stay, work authorization (if possible), etc. that a U.S. citizen spouse would have.
Your US-Citizen Eligible Family Members (EFM's)-- those listed on your travel authorization-- will also be issued Diplomatic Passports free of charge. If your family plans to take personal trips, they will require personal passports, as well (at your expense).