Hi...
I have been flying from missouri to L.A area for the last year, and I use Southwest airlines. They are the best! Always great fares, never had any problems at all. direct flights. And if you choose to fly mid week its even better. (and early in the day or late at night)
But try to get flights two weeks in advance-best prices, and watch them through the months before you travel because they always change prices and you can catch some great deals. Their frequent flyer program is great too, and they always send you coupons for free drinks! (cant beat that!)