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.
Say a person lives 78 years [9], and you take the average cost of living from BLS. Over 78 years, one spends an average of about $1.6 million dollars just to survive. Of this, one spends about $1M on housing, food, and cars ($12683 per year * 78)