Hey man, the things you should focus on are carrying weight over distance, like hiking with a pack, press ups and your torture holds like planking and wall sits. Running isn't really anything to worry about as from day one you'll be running everywhere so you'll get used to it quickly but press ups and ab workouts are thing things you will be monstered with so focus on getting proficient in those.Other that that i'd say dont focus on long exercises like long distance, light weight running, instead sort out a program of circuit training 'pump and dump' stuff, high intensity over short periods, its what will prepare you best for basic training.(Assuming NZ Army basic training is similar to USAF)
On a side note, well done for signing up