You're in luck, because traffic usually is heavy going the other way (north) in the morning. Since you'll be headed south, you'll have some traffic, but you should be okay. (If you were heading the other direction, I'd tell you to not stay so far away.) That's if you take the 405 South. You can take Lincoln the whole way towards the airport as well which is more direct but loaded with stop lights.

Assuming you're not flying internationally (so don't have to get to the airport very early), you should be fine, and will much more enjoy your stay in Santa Monica over the airport area. The other possibility, if you wanted to stay near the airport but in a nice area, is Manhattan Beach.