I just moved to SF from Canada for 8 months. I'm also 19. The process took about two months and cost over $1,000, including health insurance but not the flight. I was lucky because I'm a Canadian citizen, I'm currently attending University (took a term off to be here), I'm returning to finish my degree at the end of it, and I had a job lined up, all of which helped to make things a lot easier.

I admire your sense of adventure, and I don't want to discourage you from moving here. Just be aware that it will involve a fair bit of patience and frustration. Good luck!