John, I've always booked through Breezenet.com. By far the best prices you'll find with no financial commitment or cc guarantee. I've done this for about eight years now, usually flying west a couple of times a year to hike, and have been happiest with Dollar Car Rental - their rates are way below Hertz or Avis. and I've never had a problem with one of their vehicles in about 15 experiences.
The thing I like about Breeznet is that you can easily cancel and re-book when better rates appear. Before any trip, to Vegas or LA in particular, I'll reserve, cancel and re-book lower rates 3-4 times in the month prior to leaving.
Vegas has the cheapest rental cars in the US. A weekly car rental in LA will probably run 50% more than Vegas (but not nearly as bad as Frisco or Phoenix). I had a mid-sized SUV out of Vegas a few weeks ago for my Death Valley trip, and paid a rate of $149/wk ($258, after taxes and fees), and that was the most I'd ever paid for a rental out of Vegas in about 9 trips - but I insisted on an SUV this particular trip.
Pay attention to the total price when you're looking at a deal - "taxes and fees" vary widely between companies, and can add 40-75% more in cost. That's another thing I like about Breezenet - they list in descending order of total cost, not just the "rate".
My guess is, if you watch internet deals like Breezenet closely, you'll wind up getting a compact car in LA for (all taxes and fees included) about $300/wk, or maybe a standard size vehicle for $350/wk. I tend to book the smaller vehicles with Dollar - they're almost always out when you arrive, and they have no choice but to upgrade you.
One other piece of advice: when the price of gas rises substantially, car rental rates tend to go down. If gas keeps rising through the summer, watch rental rate deals closely the last two weeks before you leave. You may snag a killer deal at the last minute.
One word of warning: a new rental car company has popped up out west in the past year or so - Fox Car Rental. Avoid like the plague! They'll always have the lowest rates, but their cars (and service) are for the birds.
