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 $1000 a month will be a good start, depending on your lifestyle and area where you want to live, said Pinay Mentor in her article, Retiring and Living in the Philippines for expats, non-expats and returning Filipinos.
Cost of Living in Asuncion. Summary about cost of living in Asuncion: Four-person family monthly costs: 1,432.03$ (8,080,297.73Gs) without rent (using our estimator). A single person monthly costs: 411.93$ (2,324,312.02Gs) without rent. Cost of living index in Asuncion is 64.74% lower than in New York. Cost of living rank 456th out of 503 cities in the world.