A Howa 308 or a 2nd hand Parker Hale - 308 cos it is common and hence the ammo is cheap but a 270/7mm 08/ 6.5 all will do what you need easily
Don't start on deer with a 223 or smaller - later on when you get more accurate they are ok
A scope that costs as much as the rifle if not more - 3-9 x 40 or similar
Good binos (try mates' ones to see what suits you)
Do the HUNTS course at your local Deerstalkers, you don't have to join if you don't want to but it usually comes with access to a range to practise your shooting (which is important)
The HUNTS manual is good as is Lentle and Saxon's book "Red deer hunting in NZ" which your library system down there is bound to have a copy of
Good boots
Bookmarks