You may want to look at SFO in addition to LAX as your starting airport - a few more competitors at SFO these days.
As for which airport (based upon 15 years of business travel to and from):
Heathrow (greatly improved)
Charles De Gaulle (bad enough that I have been known to fly to Heathrow and take the Chunnel to avoid it)
Orly (Paris can't get airports right)
Frankfurt (too big too confusing)