Pregnancy care. The most highly trained is the ob/gyn specialist. General and family practice docs don't do operative deliveries. If you are thinking of a midwife, choose a nurse midwife that works at a hospital with OB backup.
Obstetrician. The obvious choice is an obstetrician - that's what we do for a living. Midwives are an acceptable alternative, if you are completely low-risk: between 20-34, of normal weight for your height and without any medical or surgical history of significance.
Baby's vantage point. This is not like a wedding or baby shower. There are risks involved for both of you. If you choose delivery like they did in the 18-19th centuries you need to accept the risks involved. Delivery away from a hospital setting involves at least a 1 hr delay in you or baby receiving urgent care, which can be fatal. The best trained people doing it with the best trained staff is the safest way to go.