First, go to LAX Official web site and look under ground transportation. There you'll find a list of rental companies that are permitted to pick-up/drop-off customers from airline terminals. Then do what lynn-a-roo suggests. Like Steve stated, costs are similar.
I have worn myself searching various avenues for the lowest cost for my trip in late June. If you're flying out of ATL, then chances are you'll be on a Delta flight. If you're not already, join Delta's SkyMiles club(free). As a SkyMiles member, I received an email last week where Delta is offering a discount when you rent with Hertz. Unfortunately, it expires prior to your arrival but they send these types of emails out often.
I looked at off-site car rental locations but you still have to get there and back to the airport. Some off-site locations don't offer shuttle service to/from airport so check first. For me, I won't be returning my rental until about 4PM on a Saturday and most off-site locals are closed by then. Since I don't care which rental company I utilize and car type will be the cheapest one, I may go ahead and go the Priceline or Hotwire way.
