The most important things is to check the tire pressure. The way cars are secured on trailers puts extra pressure on the tires and air will seep out. Make sure the tires are at the correct psi soon after receiving the car. Especially in the winter.
Double check all the fluids. Fluids don’t usually leak on a trailer but if there is a hole somewhere there isn’t supposed to be or if a cap hasn’t been closed all the way chances are your fluids will be low. This is because the car sits on an angle and the fluids are in a weird position. Double check to keep anything disastrous from happening.
And that’s it. Now you can wash the car and show it off. After you take care of all the licensing and registration paperwork of course.