D.B.
Having just moved here 4 years ago I would suggest moving where your children will be in a Shelby County School. We live in Memphis but our children attend Germantown schools and we love them. When we first moved here I had a child in each of their Elementary, Middle School and High School. I found them to be excellent schools with a wonderful staff and faculty.
We live at Lincoln on the Green apartments at this time largely due to sticker shock. We moved from a very small town in Texas and the housing prices in Germantown are steeper than we're accustomed to.
I don't have a pediatrician we've just taken them to a family doctor at the Forest Hill Family Practice. They are a good team of doctors and we're happy with them. I also use Dr. Laura Bishop for my OB/GYN.
I hope you find a good place to settle. Memphis seems to be in going through a lot right now and may have changed quite a bit in the last 25 years. Having moved from a town of less than 1000 to this has been an adjustment. Crime rate is high, corruption in government seems prevalent and there is talk of abandoning Memphis City Schools charter in order to become part of Shelby County Schools. But I still think that Memphis has a lot to offer and has the potential of being a great city.
I hope you find the transition a good one.