If you're flying out of STL, WN (Southwest) can take you to LAX and the Bay Area (using OAK instead of SFO). And for every four roundtrips you purchase online, you will get a free domestic roundtrip anywhere WN flies.

Another good option would be AA because they have a hub at STL offering more nonstop and direct flights than most other carriers.

Of course, you could chose a different carrier like UA (and connect through ORD or DEN) if that works better.

The above advice is sound: do your homework. There's plenty of information on this website to last you a lifetime. And welcome to FlyerTalk, shanpet.