Note that C changes over time, since the system is dynamic.
The company I work for build capacitance probes and interface circuits for the probes. These are also dynamic systems in that anyone wanting a probe is only interested in how the capacitance changes over time.
The basic interface to the "capacitor" is an oscillator. The representation of capacitance then becomes frequency i.e. as the capacitance rises, the oscillator frequency gets lower and vice versa. The type of oscillator we use is usually a Colpitts type but, given your "specification" virtually any type of oscillator will do.
The devil is in the detail of course and, to choose the best oscillator type requires more information such as bandwidth of the capacitance value changes (i.e. 1 Hz to 1 kHz for example). Desired resolution is also very important because this determines what base frequency the oscillator runs at. How far away is the target capacitor from the oscillator (wires can make some problems).
C are small, varies between 50 to 250pF
Those value changes are large when it comes to the sort of probe capacitance changes I deal with (changes of sub 0.1 pF are pretty common).
Which interfacing circuit would be the best for this situation (that
could convert C to some linear corresponding voltage)
Well, a frequency output may be more suitable as it directly interfaces with a digital circuit. You should also consider linearization of the "output" to actual capacitance. For instance, if the capacitance was used in a simple oscillator then output frequency is not linearly mapped to capacitance. Some more advanced oscillators can produce linear changes in frequency with capacitance but these will have a more limited dynamic range.
So, the choice of interface is still down to you explaining what your resources are.