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There is usually no really good way to go about buying a car as a foreign citizen. There are plenty of hurdles and red tape, and the process is usually a bit time consuming.
Having a residential address will be a big help though. That can serve as a home base where you can use to get the car registered and insured. I'd recommend buying the car and dealing with the paperwork in whatever state that is. From there, you're best bet will be to contact the DMV of that state and find out what the requirements are.
Another option that might be better for you is to investigate a buy back program. Adventures on Wheels, based in New Jersey, is one of those companies that will sell you a car with a promise to buy it back when you are done. It would probably be much faster and easier to go that route than to try and buy a car on your own.