Hospital birth and natural???

Dee
So I'm on Medicaid and I've always wanted to at least attempt to have a natural birth. I just worry if this is even possible in an hospital. I haven't had my 1st appt yet so I can't ask the doc what she thinks. After reading and watching some documentaries I do feel that we are capable of giving birth without much intervention. And no I DO.NOT FEEL THAT WOMEN WHO CHOOSE MEDICATION ARE WEAK OR ANYTHING LIKE THAT, I believe it is a choice we all make for what we believe is best. 
Any who has any of you given birth without intervention in an hospital, do you think it's do able? 
I've tried to find birthing centers etc but none are accepting my insurance