That's a good procedure, 66. One thing that might not always work so well is for meeting the transport right after the sale; if the car is in a rural area, the odds of a transport driver being in that area the next day are close to nil.
The car has to be near a big city to be able to call a transport company and meet it the next day. If that is not the case, you need to arrange with the seller before hand to help on that, or take it to a garage or other facility to be stored until a transport arrives. Then security of the car becomes a question; most tow shops keep pretty secure facilities for car storage.