I would under no circumstance fly coach on United to Australia. They divide their economy section into "economy plus" and regular ecomony. The economy plus is great, but it seems that the extra space comes from further squeezing the regular coach seats together. Unless you have elite status with them (or pay for an expensive ticket), you are stuck in the regular coach seats which is MUCH worse than other airlines coach seats in terms of space, and you will have a miserable 12 hours if the flight is at all full.
I unfortunately had to take United to Australia last year in a regular coach seat. I was originally booked a business class award ticket (using Air New Zealand) but due to mechanical problems with the originating United flight, and to United's refusal to put me on another airlines flight (because I was travelling on a free ticket) I missed my connection. The only option was to take a seat in the horrible coach section on the United flight to Sydney and then connect to Auckland, or to wait for 24 hours for the next ANZ flight. Needless to say, I have not purchased another United ticket since!
On a more positive note, New Zealand is beautiful and definitely worth the trip. I found the best source for inexpensive 3*/4* hotel bookings for New Zealand was
www.ratestogo.com (though since they are a last minute reservation site, you can only book 20 days in advance). For the shoulder season (November) they had some great rates, ie the Heritage Auckland or the Heritage Queenstown for NZ130 (or about $85 US).