If she's got good grandma's, not much
Will you be breastfeeding? Formula is expensive. Diapers, expensive. Get the huggies packs at sam's club and they last quite a while. BUT the good thing is that you usually get so many diapers and onesies and clothes from your baby shower that you don't usually have to buy anything but formula the first year. Oh and some nice pics every few months is nice too.
Do you know anyone that has just had a baby girl? Babies usually have so many nice clothes that they don't have a chance to ruin because they grow so quickly, most people are happy to give away boxes of nice clothes they can't use anymore...In my family we had 9 boys born one right after the other, the baby clothes were handed down so many times and they still look good!
Also do you qualify for WIC?