If you don't want to pay for Air NZ PE I'd fly Air NZ economy direct from YVR. If you want to fly via SFO or LAX your options are either UA from SFO or AA from LAX (Qantas only fly to NZ via Australia, the only direct flights they sell are AA codeshare)
Despite the fact I love traveling there is no way I'd be crazy enough to spend 3 hours on a plane to get to LAX, then hang around an airport, to then hop on another plane for 12 hours. At the end of the day the economy experience between AA,NZ and UA is pretty similar in longhaul economy.