Our wages in the LA area are not much more, if at all, compared to other cities where expenses are much less, and rents are half or less than in LA. But the cost of living in the Seattle area is similar to LA, except in housing. Except I don't know anyone in LA that can go out a lot to eat on $25,000 a year, it is literally a starving student budget here. Maybe the differences are wider than reported, or it's just the difference in housing costs. Our job situation here is very bad, find a job here before moving.
The low end for a studio in LA is $800, and you might not like what that gets you. You won't likely find a legit situation that is less expensive, the reason is that Section 8 vouchers (welfare housing help for the most needy) are for about $900 for a studio, and $1200 for a one bedroom. Of course, these apartments tend to be in the least desirable areas, so apartments in nice, safe areas cost more. There is a lot more inventory in ok areas for $1000 for a studio, and $1500 for a one bedroom, add $500 more for the Westside, and $500 on top of that for decent close to the beach. This is not for fancy apartments with lots of amenities. Rents are going up in LA. As people were foreclosed on, there is more competition for apartments.
Be careful, there are lots of scams, Google: Los Angeles rental scams, and rental scams.
Almost anywhere in the LA area you'll find everything you need, but it's so spread out. Hollywood is high crime and mostly scuzzy, and expensive for what it is. I grew up there, I love it, but I don't live there anymore. Pasadena has a wide variety of living options at ok prices, it's about 1/2 hour from the beach, more in traffic. You might look into Sierra Madre (adorable small town on the east border of north east Pasadena), South Pasadena (small town, safe, but can be expensive), LaCanada-Flintridge (not many apartments, safe area), La Crescenta-Montrose, and Glendale, too.
LA safety info: http://www.lalife.com
More info: http://projects.latimes.com/mapping-la/neighborhoods/
It is very dangerous to bike in LA, even walking is dangerous - even in the most upscale, safest, small town areas with a stroller. Ugh. Roommates = hassles. What are you going to do when they run up $300+ a month in electric bills over the summer for air conditioning, and expect you to pay half, when you would have been happy with $50 worth? When their friends eat/drink/use/steal your stuff?
You should wait until you're 21 to consider moving here, most landlords in LA don't like to rent to under 21's, too many problems with underage drinking, etc.