Question about my hair......?

Hi im 16 and white, I have really short hair which takes a while to grow. i love to wear baseball caps but like many other people the bill of the hat just looks so long and ugly when i wear them and it prevents me from wearing them as im a very conscious and fashionable person, however my friend who is also white but has naturally curly hair has an afro and wears his snapback hats ontop of his afro and it looks DOPE! im considering growing my hair long but im not sure how my hair will grow when it gets long, it definantly wont be in curly locks like my friends. When my hair gets to a long point the hair on the side of my head next to my temple Curls but not outwards, it curls onto my head so it looks like its stuck onto my head rather than growing out but i never grew it past this point as it looked ridiculous. My sister who is a hairdresser says i have wavy hair, so im going to try grow my hair but how long will it take to get to the point i have a full curly afro and how will i transform my wavy straight hair into an afro whilst its growing? thanks