capacitance vs impedance measurement
I am afraid no one will be able to give you an ultimate answer, since your question has uncertainties regarding the accuracy you need and the time and cost budget for the project, but I can give some direction.

Note, that impedance and capacitance measurement is not the same, and that you can't measure the capacitance with a DC voltage. 
For impedance measurement you have to use either an AC voltage and measure the amplitude and phase of the current, or vice versa. This is way too complicated for what you need.

There are readout solutions for a capacitive sensor. Google them! The two basic ideas I am aware of are to 


form an oscillator with the capacitance and measure the frequency - even digitally with a microcontroller - or 
measure the dV/dt due to a known current reference.


For 1) a precise solution could be to implement a Wien-bridge oscilaltor (+1opamp +1 cap +1 res +1 FET). Bridge structures in general are always good ideas to improve the measurement accuracy.