Proof of ability to pay, references, passport, and a signed lease.
I like to keep life simple.
If you like difficulty there is a special program where if people from a foreign country buy a business that employees a certain amount of people like a car wash, hotel, restaurant, etc they can move money to the US and get a bump up on green cards and cirtizenship for having a job sustaining business or piece of real estate.
Al Goldberg Broker
"Making Real Estate Fun"