How long did baby last in newborn size diapers? I am looking at stocking up - how many newborn size should I buy?

Don't buy too many. I also suggest buying reusable cloth diapers as they can last longer and they are gentler for your baby. During the day, I use cloth diapers so I only used about 1 pack of disposable Huggies NB before moving on to S size. Many S size diapers are able to fit newborns as well. It's better to stock up on S than NB size.