Nowadays most lenders require home buyers to put down at least 20% as down payment. One exception is FHA loan, which requires 3% down payment. 2 Bedroom houses around San Francisco, eg. Daly City, Pacifica, etc. normally cost $400,000. If you can settle down with a condo, of course lower in price.
Bear in mind besides down payment, you still need to have reserve for mortgage payment , closing cost, and some repair work. I am not sure whether you can get prequalification from a lender. Speak to a lender to find out your status.