There is no such thing as inexpensive in the car shipping business. It basically consists of numerous small companies owning from one to fifty auto transport trucks. The all find their loads on a central dispatch board. The companies that advertise are basically brokers although a few of them own a few trucks also but still broker out most of their loads. Most independents use the dispatch board exclusively.
There are a few "Boutique" shippers that ship only classics and race cars but they are VERY EXPENSIVE.
TO solicit your business the brokers offer prices that are unrealistic knowing they will not get a driver to work on the price they put on the dispatch board which is your price plus his commission. After a while they say "We need to raise the price to get a drive for your load". They knew this when they took your order but you went to them because of their low bid!
There are three things to look for. (1) Is integrity!!, (2) Is what is his commission? You should not pay the broker until he has a committed driver! His fee (He will call it a deposit) can be charged on a credit card. You will be paying the driver on delivery in cash or certified funds. (3) Is insurance. All drivers are required to have insurance but some brokers carry a policy above the drivers policy also.
Non running cars cost more to move!! Most trucks are not equipped to load non running cars.
Affecting prices are as follows.
Price of diesel fuel.
Commission amount. Some will say they will work harder for you and deserve more but basically they all just use the "Board"
Size of vehicles. More compacts fit on a truck than Cadillacs do.
Route. There are primary routes and secondary (Less traveled ) routes.
Season, Example moving a car from New York to Florida in the fall costs more than the moving one from Florida to New York at the same time.
Open spaces. The drivers want loaded miles. Empty places on the truck are bad for them.
Open truck or enclosed truck?
Open rails? There should be barriers between the decks to prevent dripping fluids on the lower tier. Not all trucks have them. If you are on the bottom you get it from above and below.
Your disadvantage is "Not Running" and "Large " Vehicles. This is partially offset by the fact that you are moving two cars at one time.
Be cautions and "I wish you good luck" DO not pay the driver until you have inspected the car and that is is in the same condition as it was when he picked it up.