I've never done a private sale/ purchase.
My current vehicle I bought from Carmax. My first experience w/ them went okay. Had it shipped in from Miami or somewhere down south. It works well for me, I turn them over every few years. That way I keep current and have never needed any sort of major repair. I take a short warranty on top of that. depending what's left on the mfgrs.
I worked in a business that kept me close w/ car dealers but mostly car dealer groups

(which was easily the worst part of my job) So I have a grasp of how dealerships make money and am able to negotiate. By keeping my turnaround at every 2- 3 years I can get a better "trade-in value". So after the trade in I pay the difference in cash. Remember that an in-house finance deal is often more attractive for a dealership. So paying cash or using your own bank isn't something you would want to necessarily share right away. Of course nothing in buying and selling cars is a one size fits all situation.