There’s major expense in setting up gear, but, as they say, it’s an investment in your health, your physical and mental well being.
Buying gear from new it’s not unreasonable for a ball park budget:
$400 sleeping bag
$400 woollen clothing
$400 stove and cooking, headlight and other bits and pieces
(How come everything seems to be around $400?)
Even with a solitary week or so tramp a year, for 10 years, that ain’t so bad. Or, stack it against the more transitory expenses of an international fling it’s not so extreme. And once you’ve got the gear at least it’s reusable.
Actually, in keeping with the NZ making-do way you can always start somewhat compromised and build up the kit as you work out exactly what you need.
The next biggest expense is transportation and accommodation each side of your trip, and, I guess, that varies considerably as to where you are from and where you are going.
Food and fuel is more predictable but will depend on your preferences. You can pay $12 for a commercial dehydrated dinner, or cobble something with sufficient calorific value from a base of rice or spaghetti.
Hut passes or tickets, well, you can work that out easy enough.
All in all that’s not a whole heap of help.