Hiya! I live in Budd Lake and I'm happy to talk if you want an ear. I'll try to answer some of your questions here, but it might be easier to talk on the phone. The most important things when looking to have a natural childbirth are 1) finding a provider that is on board with what you want and 2) doing everything in your power to stay as low-risk as possible. You can have an intervention-free birth anywhere- hospital or home, but it is imperative that you find the right provider and stay as low-risk as possible to do so. That means working on your nutrition and exercises, and taking classes or refresher classes or reading books that will help you toward your goal, and really being an informed consumer.
How much you'll really end up paying the midwife depends on your insurance. The pricing usually includes all the prenatals, the birth, and postnatal visits. I can't stress enough that a good birth and a good midwife are worth the cost for you and baby. Remember midwives spend WAY more time at prenatals, at your birth and at postnatals than traditional obs. They really are part of your team and on your side. I think I had to outlay about $3000 for retaining the midwife, but that was over several payments, and after the birth Aetna paid her a certain amount and she gave us back somewhere between $1000 - $1500. For a comparison, the birth of my first child who ended up in the NICU for 2 days cost me $2500 out of pocket and I had dual insurance. The birth of my second with single Aetna insurance, no NICU, and we left at 26 hours ALSO cost me $2500 oop. So in reality even with buying the supplies I needed for the birth (about $200-$300 including buying a $30 deep kiddie pool for my waterbirth so we could just throw it out after) and the midwife fees it actually cost me LESS for a homebirth.
Midwives do all the normal baby checks for apgar, weight, length, etc at your home and usually come back within 48 hours to run the heel-stick blood tests and to check up on you and baby. Barring any unforseen complications you don't have to go to the hospital. Talk to your pediatrician and explain you will be having a homebirth and find out when they would like to see the baby following the birth. My ped wanted to see the baby within 48 hours of birth, though we ended up seeing him more like day 10 or 11 because of the holidays and crazy weather.
I hope that helps a bit, and if you want to talk message me and I'll send you my info!