Hi,
There's much to look into for shipping a car from the UK to the USA. The biggest issue is that a right hand drive car needs to be over 25 years old in order to be imported to the USA and used on public roads there. If you wish to ship a RHD car over and keep it on private land and not use it on the public roads, I think you are allowed to do that if less than 25 years old.
If the car you are taking over is Left Hand Drive, you'll need to check it's 'specification' and see how much of it complies with US legislation. Chances are, a lot of it's emissions, safety equipment etc will be the specification of it's intended market/country, so you'd need to have the car federalized - which can cost a lot of money.
Usually, you'll find it's only interesting and sought after cars that are imported to the USA where they weren't officially available via whichever manufacturer it is. This also means the potential big costs for making a car USA road legal is offset to the value and rarity of the model it is.
Here's a link for you to begin researching if it's worthwhile or not to continue with your idea
http://www.gnkauto.com/Cheers, DtM! West London & Slough UK!