The US immigration system is a minefield, it's worse than ever at the moment, so good luck!
If you want to live and work in the States, you will normally have to get the job first. If you come in on a tourist visa, you can't then change it to a work visa, you have to go home and come back. The type of visa you will get depends on the job and the employer.
An easy way to get in is to write to the British Embassy in Washington and ask if they are looking for any staff. You don't need a work visa to work there as it's British soil :)
If you want to get a mortgage in the States, you will need to have built up your credit rating. It takes a minimum of 6 months to do this and you have to work at it, use credit cards, pay bills on time etc.
Anyone can buy a house, you don't have to be a resident, just be able to pay for it.