For safety, uh, it's LA County, it's not really safe by the standards of most of America, but you can go online to the LAPD website, find the neighborhood, and view crime stats as well as read through what crimes has been happening in a particular neighborhood recently. Doing so should dispel any notions of safety in all but a few areas.
The rental sites are all good and well, but when I lived in the LA area I had to find apts. for my employees and many times the properties listed were already rented and I became very frustrated.
Truly, your best bet is a realty agency that has a dedicated agent doing residential property management. Being that you are new to the area - an agent can provide you with a real-time list of properties. Al within the parameters you specify.
Dealing with the net is convenient and can give you insight to what rent is averaging - but only a human can give you the quick feedback you will need.
The good news is - this service is typically free! Don't shy away from an agency just because you think there might be a fee involved. At best, you will have to pay an application fee once you find the place you just must have!
If you are still confused or need additional assistance - send me an email and I can get a reputable firm to contact you directly!
Good luck to you and I hope you enjoy So. Cal. its a great place if you stay safe and take care to be careful!
westsiderentals.com (pricey but they've got the most up to date listings--see if your company has a corporate discount)
craigslist (free -- lots of listings but not as many as westsiderentals.com it seems)
apartmenthunterz.com (waste of money--they've got a lot of stale listings. i called a bunch a places that said they never even listed with them)
if you decide to subscribe to a rental site, make sure you set your initial search settings to be very specific. This is so that if they have a guarantee, you can try to claim that they can't find sufficient listings that meet your criteria and you'd be able to get your money back if you are unhappy with the service. i made the mistake with apartmenthunterz.com.