Back in 2007 when I got my Pinto Wagon it was 400 miles away in San Francisco. The guy I bought it from was a Steward for Southwest Airlines and as an incentive for me to get there and pick the car up (he had to frequently move it due to street parking issues) he gave me a free buddy pass to fly up. Thus, my trip was one way. U-Haul was by far the cheapest but I was required to rent their 10 ft. box truck to pull their car trailer.
The rental was $240 for the 24 hour period, gas ($4.25 a gallon at the time) at 13 MPG was $150 and other incidentals added up to $425. I'm not sure if likely increased rental rates would be offset by cheaper gas now. I had looked into having the car shipped. There were a number of issues. One was access through tight San Francisco streets. Second was concern about the car starting and being able to be driven onto the carrier.
I had read horror stories where the standard contract had a 30 day delivery. Cars would be loaded/off-loaded numerous times as certain drivers were only going "so far." And the next guy to get your car closer to you was always looking for the meat on the bone. I read where cars just sat in the middle of nowhere because drivers were not interested in taking the haul. In some cases the car owner eventually drove considerable distances to get their car only to find it had accrued considerable "storage" fees.
It was at that point I opted to transport the Pinto myself. THEN..., I began to read horror stories where instead of getting the U-Haul 10ft. box truck to tow with people were getting 24 ft. trucks with 325,000 miles that often broke down! Thankfully I did get a 10 ft. truck with only 7,000 miles on it and all went well.
So, be weary of low cost shipping. And, the "deal" a car might be can be quickly offset by the cost to transport it. Especially cars that do not run, or cars the transport "claim" wouldn't start and now want additional cost to complete the transport.