I strongly agree with Mute's point about separating home ownership from pure investment in real estate. Obviously, you want to get a good deal on your house and have it appreciate. But if you're buying a home to live in, you don't want to worry too much about trying to guess which may the market's going to move. It's guesswork at best, and if you let it anxiety about whether your "timing" is exactly right can leave you frozen on the sidelines for years. Buy something you can afford and that you like, and build from there.
As far as an agent, you want someone who knows the area you're looking in and who you're comfortable with. Sit down with them over coffee and interview them as you would any other professional. Buying a home is both a major financial investment, and also often a very emotional process. You want someone you trust and feel comfortable with.
Renault's posts are fairly old, so he may have moved forward with his process. But if he or anyone needs recommendations for an agent on the west side of LA, I know a couple of good, trustworthy people. I have no connection to them except that they are friends I think highly of (and one was my agent when I bought my current house).
Also, someone suggested looking in the West Adams district. That's a fascinating neighborhood with beautiful historical homes, but has its pro's and con's. If anyone is interested in the neighborhood, a colleague and good friend of mine would be a good resource. He has lived in the area for 5-10 years, and during that time has bought, renovated, and resold several historic homes in the area over that period (once or twice simply to save them from people who wanted to gut them and turn them into multiple-occupancy buildings or churches). He would give you frank insight into the pro's and cons of the neighborhood, and probably would be willing to give you a tour if you were seriously interested. I also know slightly, through this friend, a real estate agent who specializes in that area.
Finally, in response to a question posed and then halfway retracted by Renault - I would be leery of buying a home downtown or anywhere else because you're speculating on appreciation. Downtown is especially dicey for a variety of reasons. But if you're buying a place to live in rather than as pure investment/speculation, the most important thing is to buy a place you'd want to live in. You never know which way the market is going to go, and you could end up living in the place far longer than you initially envision.