I would start with one box of newborn nappies. If you are going private, you do not need to supply your own nappies. It all depends on what size your baby is when they are born. We only needed one box with DS2.
You can try Nappy Land outlets for Huggies, which I have found the best branded ones. Aldi ones are excellent and they now have a proper newborn size. When they first started with nappies, their newborn was a big weight range and I found didn't suit a real newborn. If you have any left over, you can either give them to friends who have girls with baby born dolls (cheaper than baby born nappies Lol!)
You can google nappyland, it brings up their locations.
We are Costco members. Not just for nappies, we also get wipes, tissues, toilet paper, vegemite, diced tomatoes and alot of other things.
HTH