Rainy.
If you buy or rent, one of your main problems will be insurance andemissions.
You may want to go to a state that willallow you to get a drivers license in order to buy US insurance. If you rent, it'll include the insurance to liability for the car. YOu might have to pay a premium. It might be cheaper in the long run to rent.
If you decide to sell the car, then you might not sell it depending on where you do so. Most states have different permissible emissions levels and I'm betting that as a tourist, the amount of money you have will be for a very cheap car. Cheap cars usually just meet local emissions. Say you want to sell in california after having bought in Montana, chances are that you won't meet emissions and will have to sell for a lot less.
That said, the smaller states can hve some pretty good deals. Factor in about a week in your first stop to make a good purchase.
Also remember to take along any proof of having driven or insurance in the UK. It will get you a lower rate if you insure over there.
One of the best tips I've ever heard is to wear a kilt for hitchhiking and pubs.
Even if you don't have a Scot's accent, you are different sounding enough to make a difference. People will pick you up (In both places!) just to speak to you. Almost everyone in the states has an aunt/uncle/grandma/etc 15 times removed who was from scotland. ("Do you know my cousin Jeff?")
US GUYS, do they still do the $50 monday night flights on southwest airlines?