Agree with everyone saying to move to the city proper if you're going to move. You can do it if you're smart and tenacious. You have to be ready to have your mettle tested if you're moving to this challenging of a city alone. I moved here on less than I should have almost two years ago. It would have been less stressful and smoother if I had came with better reserves, but I learned so much from the experience, I don't think I'd do it again differently.
Save up 3-4 months rent at the very least. Aim for $900/month. However, there are shared rooms to be found in the $700-800 range. There are also cheaper, but they get scary (from personal experience). My first landlord actually found me through a "Room wanted" posting on Craigslist. So, after reading enough to figure out what's realistic, put up a description of what you're looking for.
Housingmaps.com and Padmapper are your two best friends for finding places. They both map craigslist postings with varying results, but easier to find visually and see what's new everyday. (I got my current place, which is amazing, by catching the listing in the 2-hour window it was up and securing the first tour right away.) Couchsurfing.com and Airbnb.com offer brief launchpad options if you need to move first to hunt, which is likely since people looking for roomies are picky enough as is and not being able to meet in person is a huge drawback. There are also decent hostels in town that range from $30-40/night for your apartment-hunting HQ, but you need to have a plan and be aggressive. Watch out for SROs. Google them, but you don't want to stay there. A lot of them show up on Craigslist. Cross reference every place with the bed bug registry. Seriously. There are some dirty places in this city.
Here's my personal take on ideal neighborhoods. I think the Divisadero area near Haight is very cool and it's been gaining popularity since I first moved here. Diverse and still a little rough around the edges. Alamo Square has some good room finds and is in the middle of a lot of cool neighborhoods. Every direction is something pretty different. Lower Haight is cool and there are some cheaper rooms on Fell and Oak since they're noisy with traffic and sheltered folks find them "thuggy." Hayes Valley is pretty, but half of it gets dead at night. The Mission gets labeled as Hipster, but it's just a younger crowd in general. Lots to do, but in high demand. Noe Valley is sleepy, but some people really like it. If you ever find something in your range around Church and Market, jump on it. That's area has a lot in terms of nightlife, transit and groceries. I'm not as big of fan of SOMA or TenderNob. They're more city and less residential. Just not as uplifting when you step out your door. Richmond and Sunset are cheaper, but it's almost like living outside the city when it comes to transit times.
For jobs, it can be a tough market to break in, but new stuff shows up every day. A lot of good companies use Craigslist and you should be visiting that more than a few times a day. Indeed.com is like a good for jobs and you can easily set up alerts that email you new listings by keyword everyday. Be creative with keywords. For example, if you have a specific degree or type of experience, search for that instead of just job titles. Build your LinkedIn as much as possible and find out who you know where, even distantly. A lot of people use it here, so it's easier to find your degrees of separation. Also, this depends on your background, but get some personal site up that shows a little of who you are and organizes your social links. Flavors.me is a good one. You don't have to be techie, but it seems like employers here gravitate toward nifty people who look like go getters. Something tangible that shows this is a bonus. Also, save a budget for just going out to meetups in your field. This doesn't mean just going to industry networking events, but social stuff that will start building your relationships with people who are at companies that have jobs for people like you. My housemate was extremely active this way and got his dream job within two months with just his degree and no experience.
As for social scene, I think sf.funcheap.com keeps the best track of interesting events in the city.