It's generally not recommended to rent a car from the airport. Too expensive and overpriced. Especially if it's at LAX
enterprise alamo hertz nattonal, all have rental counters at the airport, also there are a buch of others just outside the airport grounds, they all have web address
I'd try Hotwire or any other of the discount sites. Cars are going to be cheaper for a weekend deal although if you need it for a week you could possibly find a good deal. Sunday thru Thursday are going to be your most expensive. Failing booking online, try Enterprise or Dollar. They're second tier rental agencies and shouldn't be nearly as costly.
You get enterprise. There are usually car rental places at the airport also