There is no way to obtain the legal authorization without employer's assistance, other than getting US residence through family ties. So the best way for you is to first get employers interested in you, enough to apply for a work visa.
A budget of $1000 a month will be a good start, depending on your lifestyle and area where you want to live, said Pinay Mentor in her article, Retiring and Living in the Philippines for expats, non-expats and returning Filipinos.
Cost of living in Davao is 70% cheaper than in Honolulu; Cost of living in New York is about the same as in London; Cost of living in Melbourne is 14% cheaper than in Sydney; Cost of living in Kuala Lumpur is 53% cheaper than in Singapore