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.
The cost of living is in Puerto Vallarta is definitely less than the cost of living in the States. The cost to rent a small apartment or a condo unit is 3,000 pesos to 5,000 pesos (about US $170 to $282) a month.