Shipping can be quite variable. If the car is in or near a big city, then using a broker is probably going to be fine; there will be plenty of truckers rolling through such an area regularly and someone will very probably pick it up in a few days. The price quoted up front by a broker will probably hold in that case.
If rural, it may take some time to get someone to pick it up and don't expect the broker's inital quote to hold; be prepared to pay a few hundred $$ more or it may not happen. Whoever gets it will have to take the extra miles to go get it.
If the car is supposedly running, then OK. But make darned sure somehow that it IS running, if you tell the transporters that it runs. If they show up and it is not running, then you'll in for a bunch more money. I just bought a car from a guy in eastern VA who bought the car from CA a few years ago... the car was sold to him as running but was not when it came time to pick up and, it took weeks and a lot more $$ to get it shipped.
Door-to-door has the car going to the least amount of locations, but it has its possible issues. Pick up can be a problem if the seller is an individual and they work regular hours. Someone has to be there to get the car and keys to the driver, and the drivers don't always show up at a convenient time or even at the scheduled time. So if the seller can't take off as needed, then there are sometimes ways to have it dropped to a 'terminal' with some shippers. A 'terminal' is often a towing lot with a secure fence so is probably OK. But find where the terminal is and look it up; I found one 'terminal' near Roanoke VA it that is just a gravel used car lot with no fence! (I try look at the camera view from the highway on Google Maps to see waht any such 'terminal' really is.)
Drop-off can be the same way; schedules are not guaranteed in many/most cases despite what you may be told. So you have to be time flexible on your end, unless there is a good nearby 'terminal' to use.
OBTW, if you ask for shipping quotes online, expect to be bombarded for weeks with emails!