In terms of fare, United, Air New Zealand and Qantas will all have the same sale fares around the $700 mark starting probably in February. Watch out particularly for United - every so often they have fares to Oz for $800 from the East Coast and $500 from the West Coast.
In terms of travelling, I would always say travel through the night. From the US that means leaving on the evening flights, and from Australia leaving about noon Sydney time. Because the flights are twice as long as the trans-atlantic flights, the daytime travel becomes farely wearisome. In addition, I've found that a day of sunshine once you arrive followed by a good noghts sleep is the best recovery technique from jet-lag.