The quickest way to get a large volume of rentals to compare at one time is to use Expedia (
www.expedia.com). Select CAR (ONLY), enter your dates, and don't enter any preferences. By not entering any preferences you'll get every car rental company near LAX. Be sure to look for a car company that is at the airport or very near to the airport with shuttle service to their rental car lot.
I would choose Expedia first. I would search online and not by phone because you'll get lower rates online.
You may want to research on Expedia and afterwards go directly to the rental car company's website.
Another option is to logon to
www.rentalcars.com Rentalcars.com is okay but be sure to read the terms carefully. In Hawaii, I had to pay a non-refundable deposit or the entire rental through rentalcars.com, maybe that's their policy just in Hawaii. I believe I've rented from them on the mainland too, but I don't remember having to pay deposits for mainland rentals.
That's my advice. I'm a Secretary and I make lots of car rental reservations for business and personal use. Of course, for business we have contract rates with many of the car rental companies. If your company doesn't mind you using their discount, then by all means use your company's business account number when making your reservation, just be sure to pay for full insurance because you don't want the rental company to come back on the company you work for in the case where you might have an accident or worse yet...Total the Rental Car. You might put your job in jeopardy.
P.S. Check out the gas prices in California before you rent a car...this information may help you decide on the size of car you want to rent and the amount of gear you have will decide the size you'll need to rent. I drive a car that takes only premium and my last fill-up (last week) cost $4.39/gal. Also, if you drive Hwy. 99 in fog you may be glad you rented a large car because you'll be safer if you get into an accident. The Fresnonians, like Steve C., can tell you if Hwy. 99 gets lots of fog in July. You really don't want to take I-5 to Fresno, the gateway to Yosemite. Hwy 99 is much more scenic.
Have fun and post pictures and your road trip when you return to Georgia.