I would fly via San Francisco rather than Los Angeles as it is a much easier airport to transit and if I had a stop-over, I prefer San Francisco. I've flown Sydney to New York via both and there is just no comparison in the time taken at each airport. The last couple of trips, I didn't have a stopover, preferring to get it over in one go, but it usually takes me a couple of days to get over the flight.

One thing you need to consider though and that is buying your flight tickets early. My son flies home each Christmas and finds he needs to book fairly early in the year as seats go quickly. He flies United as they are far cheaper than Qantas. I think he buys economy and upgrades with points - if possible, business class is the only way to go for such a long flight. I must admit Qantas have far superior seats in business class, but I can't fault United's service.