I'd say there is no best time to move to LA. Any time is fine, although it does get hot in the summer. If you're going to be moving boxes, prepare to sweat.
If I were you, I would try to line up a. Job before you move. Jobs are pretty competitive here. Even getting entry level work, you're going to find that the pool of applicants is pretty large. It may take you a while to find something. It really depends on your experience.
Also keep in mind that a huge number of younger people that live here re sharing a apartment with a roommate. Rents here are very high and unless you have some good cushion in your savings, you're going to run into some trouble financially. Los Angeles is notorious for making people move back home after they couldn't find an opportunity here.
Even if it might not be possible to line up a job ahead of time... At least make some connections with some business owners. Write to them online and ask for advice. They may be able to tell you how to get better prepared, where is best to look, or may tell you no now but offer you something once you're here. Connections are really the most valuable advice that I can give you.
Hope that helps a bit