Simple variable Capacitor circuit to feed ADC
The way to to this with an absolute minimum of support circuitry is to use a DIO output to charge/discharge an RC circuit consisting of your capacitive sensor and some resistor to produce a time constant that makes sense for your application.

Start with the DIO low, leaving enough time to bring the resistor voltage to zero.  Turn the output on and start a timer at the same time, and time how long it takes for the resistor voltage to reach some predetermined level.  Many microcontrollers have a comparator peripheral.  If you use one of these, you need NO external parts.

I don't believe the Pi has such capabilities, but an external comparator is not that big a deal.

Indeed, the need to build circuitry to create an analog voltage proportional to capacitance isn't the best way to go.  the methods I like most for capacitive sensors all involve counters, not ADC's.  If this isn't Pi-friendly, adding an 8-pin microcontroller to use the technique I describe, and then generate a PWM signal that you can capture with the Pi.

You can certainly use the circuit in the answer you point to (with suggested modifications as described in answers, as the original won't work), but it's parts intensive.  It's also nonlinear, and you would need to use a curve fit or look up table to get your capacitance value.