I just noticed that you are in New Zealand, and I am not sure what your fly needs really are, but it occurred to me that what you are looking to fly with is the also probably the easiest to dry rent.
Here in the states, the airlines have really cut back on checked baggage, or upped the fees for additional bags/mass. I think the fees for bringing your own may outweigh the cost of rental for the same. Just a quick check of one airline here in the states, shows they now charge $25 each way for the first checked bag per ticket, and $35 for the second bag. Additional bags are $100, oversize/overweight bags are $150 each way.
Renting seems far more cost effective, at least up here in the states.
Jay