Most single-vehicle moves go on a tilt-bed or beaver-tail lorry. The bed tilts to ground level, so a car can be winched on even if it doesn't run, and low bodywork clears without damage.
Non-runners, classics, track cars, prestige vehicles and auction purchases are all routine work. Tell the operator whether the vehicle starts, steers and brakes — that decides whether it's driven or winched.
For several vehicles at once, a multi-car transporter is cheaper per car. For very valuable or concours vehicles, ask about enclosed transport.