i would say at least a dozen to start. eventually 18-24 would be best in case there is a day that you cannot do laundry.
and bum genius one size are great, just be prepared that they may not fit your newborn. we used disposables for the first month b/c of the size issue w/ cloth diapers. and also b/c of the umbilical cord and circumsision. we now use cloth and, like you want, disposables when we are out or w/ a babysitter.
do your research about cloth and washing them. there are some detergents that you can use and some that you can't. dreft gave my baby horrible diaper rash and i had to 'strip' the diapers. the most convenient detergents are purex free and clear and all free and clear. here's a website that goes over it www.pinstripesandpolkadots.com
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