If you are transporting a single car, a small to medium flatbed trailer will provide plenty of space. In some cases, you may need something a bit larger or even a dually (a heavy-duty consumer pickup truck with an extra set of wheels in the back). Keep in mind that a larger truck and/or trailer will come at a higher price tag.
The company you work with shouldn’t expect you to be an expert, so let them help you determine the recommended solution for your vehicle based on your needs.