I was in your position just over a year ago in the same area. Yes, World of Strings and Lemur are good 'retail' places but you'll get much more bass if you go used. A good place to try out some aggressively priced stuff, including new stuff is BassesRUS in Pasadena. Lots of entry level stuff but some interesting others ([Invalid or Expired Link Removed]).
Other than that it's all about Craigslist. You can use Search Tempest (searches all Craigslist listings in the area radius you select. I did have to drive a bit but eventually have found a real nice Meisel laminate from a pro for $1100 (cared for by Lisa Gage at Bassworks) and a 1950's Kay M-1 for $300! I had to put another $600 into it for some repairs but now I have two very nice basses for under $2K and easily sellable for twice as much.
You'll quickly learn the brands as many have described in your responses but like many have said, you just have to try some. Being new, you won't really know what to listen for. I didn't. And the kind of bass you buy is highly dependent on the kind of playing your going to tackle. Jazz, Bluegrass, arco, pizz. Heck, I played some $40,000 Pollmans and thought they sounded like crap next to a Chinese house bass at Lemur...but that's because I didn't bow at the time. But I played a killer consigned bass at World of Strings that was $1,800 that sound better, had a pickup and had more character than 6 others there that were over $3K.
I, for one, love the chase of a cool instrument. PM me your email and since I look everyday, I could point you to some worthy listings. But every bass has it's own story. Some could actually be great instruments but horribly set up (which is the most common culprit). So, if you are lucky enough to stumble upon one that is set up nice, you like the tone and looks, and the price is right...just try not to pay retail cause your tastes will evolve and you will likely need to sell it to pay for the next step up.
Being new, I most appreciated ones that were set up nice. Make sure you get a bass with a adjustable bridge. You'll need it as you improve.
Good luck!