La L:
We started one of these back in 2011 or so. We are a small, family-owned, Midwestern community bank, so we didn't do the FFIEC-defined BSA nightmare private banking. We did what RC described, with a special DDA and a few more HELOC choices. The main difference between private banking and personal banking in our bank is that the private banking customers have one direct contact for all of their needs. A little more hand holding, if you will. Oh...and their checks say "Private Banking" in a fancy font.
I know I got some good advice form the threads back when we started. Feel free to search my screen name or just shoot a question back.
We were fortunate in hiring an experienced banker. Our management was also very open to discussing the advice I got here. We had several discussions about the requirements for Private banking, possible impact, and possible exception requests.