It is really hard to know, isn't it? DS2 was 8lb 13oz at birth and didn't fit any of the newborn nappies I had bought at all. He went straight into smalls and fitted some mediums by a few weeks old. I had about 25-30 fitteds and 8 wraps for him.
DS3 was expected to be 9lb + so I didn't bother to buy many NB again. He was only 7lb 2oz though! I had to stock up on Newborn quickly.
He fitted his Newborn nappies until he was about 10 weeks old. Again I had around 25-30 nappies and 6-8 wraps that fitted at anyone time.
As people have said you have lots of time to build up a newborn and small stash. I tried to get the small/NB stuff cheaply and nothing very fancy because as you say they grown out of them so fast. I saved my money and bought some nice medium things which fitted for much longer.