One of the most important things you need to do with your first child is pick the person to deliver them. Most couples tend to go off of referrals, whether they are referred by a friend or family member, or their own doctor practitioner, referrals are very common. Most family physician doctors will tend to refer you to obstetricians though. However, a new trend is developing with new parents, in which interviews are held with prospective caregivers. This is an excellent way to feel out your potential candidate. Having interviews with doctors and other caregivers enables you to ask them questions you feel need answering, and whether you feel comfortable with them or not, because it is very important that both you and your partner feel comfortable with your caregiver.
There are however, caregivers that aren't doctors, called midwives. Midwives are licensed nurses and midwives through a national accredited center of learning, so just like a doctor, they go to school to learn what they need to. Midwives are very popular in Europe, and show a growing popularity in the U.S. due to the intimate relationship that can be built with them. Midwives are better for taking the time to answer any and all of your questions, provide a more natural and less routine birthing experience, make less interventions due to routine, and because they will support the mother in whatever birth experience she chooses to go through with. They are also available to talk through with all the emotional changes that go through with pregnancy as well, to both yourself, and your partner. Another big plus with choosing a midwife is that they tend to have a lower rate of cesarean section.
You should also consider the setting of where you and your partner want your baby to be born. If you want family and friends around, you might want to choose a birthing center, which is staffed entirely by midwives, or even to have your baby at home, by way of a midwife. However, having the baby in the hospital also has it's benefits, such as the epidural, and if anything goes wrong, you're already at the hospital with no need to transfer there. You can still have the midwife perform your birth at the hospital, with doctors on hand if anything out of the ordinary happens.
Picking an Obstetrician-Gynecologist, or a midwife will only be an option for you if your partner is healthy and isn't having a high risk pregnancy. Midwives will then defer you to a doctor, in some cases a perinatologist if it's serious enough, or if they're having multiple babies. Remember, this decision is as much yours as it is your partner's, even though she is having the baby your concerns are just as important.