Welcome to the forum TP1
16 years is a long time ago and, if you've had a clean record since then, I'd think you would still have a good chance of getting into NZ if everything else is in order. If there is any question of problems with your previous record, perhaps if you could convince NZIS that it was a 'folly of youth' that brought about the offences, they shouldn't be too hard on you. Also, if you didn't get a prison sentence, that should go in your favour. I'd say push ahead with your application and don't worry too much about your previous offences. If all else fails, you could always apply for a character waiver.
Read through
this and
this to see how it affects you. The second one mentions drugs and waivers.
Good luck.
