As a ballpark only (as it's not in Wellington), All Secure has a 'travellers' deal on their website which is $40/month for a 1 metre cubic Self Storage locker.
So given your "$50 or $500", the answer is $50 - although I suspect you may find that most places will potentially charge a little more if you're only looking for a single month. I have a storage locker in Sydney, and it had a minimum 6 month term on it in order to get their standard prices.
Depending on how you're planning to use it, keep in mind that most self-storage places will be outside of the downtown metro area, and may not be that easy/cheap to get to if you don't have suitable transport. You may be better talking to a hotel or (more likely) a hostel/backpackers and see if they will store it for you.
Alternatively Wellington Airport has luggage storage, but it costs ~$10/day.