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.
Food and drinks are very cheap in the Philippines. A regular individual spends around 200 euros every month. One can eat in middle class restaurants every day since each meal would roughly cost 3 to 4 euros. There is also more expensive food in hotels and fine restaurants that can reach up to 150 euros for a meal and accomodations.