Driving the west cost of the USA?

Hi there, myself and partner are planning to drive from Seattle down to Arizona at the beginning of March. We've got no time constraints so plan to take our time and see the sights. We were wondering whether it would prove better financially to rent or buy a car to do this. I understand that insurance may be quite expensive for foreigners and buying a car may be difficult if are not a resident. Does anyone have any information on this. I have also heard that you can drive cars across states for people and wondered if this may be a possibility. Also we are not planning to pre-book accommodation, but rather stop in motels etc along the way and leave the schedule flexible. Does anyone know if accommodation is fairly easy to find generally and how much you can expect to pay for a cheapish motel? Any advice greatly appreciated. Thanks.