I am traveling to New Zealand in december and have the choice of budget, standard or premium insurance and i don't know if it's worth the money buying the premium, however the budget doesn't include 'missed departure'. Does that include if you are changing over in a different country and your first plane is delayed?

http://www.statravel.co.uk/blue-cover.htm

"In the event of the Insured unavoidably missing the pre-booked departure of
the outward journey from the U.K./Eire or the final return journey to the
U.K./Eire due to the failure or disruption of pre-booked connecting public
transport, to reimburse the Insured up to the Sum Insured in respect of the
cost of necessary, additional, receipted, travelling expenses incurred if the
Insured is unable to reasonably reorganise the travel plans and is as a result
stranded at such final departure point."

Missed departure only includes the INITIAL departure from the UK - but it CAN be argued it covers the WHOLE of the return trip - it depends on whether you can argue that 'final return journey' can be in two or more stages.

(Make sure you enrol with Medicare if you need medical treatment when you get over there.)

The premium policy has a few extra features but you don't need the extra medical expenses cover if that is your concern.