Advice on getting a stable analog reading of capacitance
Capacitance sensing may not be the easiest option. The measured capacitance may depend on things other then the distance to the hand. Ultrasonic sensors might be a better choice.

That said, if you do want to go down the capacitance route, you probably want a Capacitance to digital converter. An example would be the Analog Devices AD7745 or AD7747. Both are based on the same delta-sigma core, but the former measures the capacitance between two plates, and the latter measures capacitance to ground. Other makes and models also exist.