Ok dude I'm from the Bay Area and have lived here my whole life, here's the down low, if you don't work for Google,Apple, or some other big tech firm, you can't afford to live in SF. Period. Particularly given your hesitance to stay in homeless shelters, not that I blame you on that score. The city is going through major upheaval and gentrification at the moments and all the prices are only going up. You wanna be where the real action is and the NEXT big scene will be? Move to Oakland, it's much much more hipster than you think it is. You can Bart into the city from most places in Oakland and Bart is gonna be your new best friend btw.
If you really don't want Oakland your next best option is Novato. It's a town about 45 mins north of SF, no Bart but there are busses and a ferry. It's the last reasonably affordable section of Marin and you can definitely get an apartment for less than $1000 a month, and less if you get a roommate. Nice town, little crime, low prices.
As for a job, either get a second one or a new one, you will not be able to self support on a part time job in the Bay Area, it can't be done. San Rafael, town next to Novato and closer to the city, has a large warehouse district called the canal. You can probably find work down there in one of the auto shops or warehouses, they are usually looking for grunt labor. If you have any experience with bikes, there are many bike shops around the Bay Area and usually pay ~$12/hr, and when you can afford one GET A BIKE. Bay areas a crappy place not to have a car, but a bike and strong legs will get you where you need to go for relatively low maintenance costs. (Popped tubes mostly from thorns)
One thing to keep in mind, for the most part, Bay Area people are super civic minded, and really like feeling like they are the solution to whatever problem. Show people your a hard worker, responsible, and just down on your luck and they will probably try to help you in some capacity. That's a double edged sword though and they are people who will quickly move on to easier more satisfying causes so you need to be able to pull your end.
As for everyone here saying you have to move back home, I disagree. You have not done yourself any favors here but with some minor adjustments your plan is more doable than many of these non locals realize. Just forget San Francisco entirely as anything other than a place to work or visit on weekends. You will be lucky if you can afford to live there by the time you're your dads age.