If you are giving birth at a hospital, you will probably be able to choose whether you want to be under the care of an OB/GYN or a Certified Nurse Midwife. If you and your baby are in good health, you will be able to choose whether you want to give birth without pain relief or with the help of epidural anesthesia. Giving birth in a hospital often means you will be bound by strict policies, but you will also have high quality care available if something goes wrong. If you need to have a scheduled c-section for some reason, the hospital and an OB will be your only choice.
There are various types of birth centers. Some are located on hospital ground, while others are free-standing and not associated with any hospital. Birth centers are a good option for women who would like to give birth as naturally as possible, while still being out of the home. Birth centers are normally staffed by midwives, but those that are inside hospitals tend to be more medically minded than those that are independent.
Home births are a viable option for women who have healthy, low risk pregnancies and who want to give birth naturally without pain relief. They certainly have some advantages, like being able to stay with your newborn without interruptions after the birth, and lower rates of maternal complications such as hemorrhage. Home births are sometimes cover by insurance, and can be attended by various types of midwives depending on your state. You might also want to take a look at rupture of membranes when your water breaks, and what is a birth plan?