That's a solid double major to start with, but I would pick statistics over data science. Stat masters degrees are super valuable and increases your chance of getting a job. Not saying data science won't, I've just found it easier to get people jobs with stat degrees. Also, living in NZ isn't a big deal, but you might want to apply to some American universities. Or you can try to find an entry level job, come over and work, then get your masters. That is something you see in the field a lot. Send me a link request and let me know when you are looking for a job.
Do you graduate in the spring? If yes then you do not have to start applying yet. It's always good to make connections though (which I'm sure you know). Send me a linkedin request Tom Wright.
You probably know this already - maybe you can consider looking into the MOOC courses on data science to get yourself a head start in the university program. Coursera offers a very decent Data Science Specialization program from John Hopkins University for 470$. There are also a bunch of other free courses/materials online.
Good luck to you too :)
Best of luck.
Data engineering is definitely more in line with my background and experience, though data science is fascinating to me and something I'd like to learn both for my own edification and to provide better support to colleagues in any future data-oriented roles.
Thanks for the blog recommendation, I'll take a look. I did just pick up Data Science from Scratch to get me started and I'll go from there.
Thank you very much for the thoughtful feedback and recommendations!