There is Nyquist law: sampling frequency should be twice signal frequency to exact rebuild sampled signal.
Practically, for better performance, for signal 10kHz use sampling frequency bigger than 20kHz, maybe 25-30kHz.
It is completly depends on your dynamic range and antialiasing filter sharpness. more dynamic range( number of ADC bit) requires either shaper antialaising filter or more sampling rate.
Exact reconstruction will occure if you have infinite number of samples.
This business with Nyquist criterion only gives us the minimum frequency (2 x Max frequency in original) at which you will be able to "follow" the original.
In practice, if you want the reconstraction to be of good quality take as many samples as you can .. obviously be reasonable and don't exaggerate.
I think in your case of 10kHz something close to 100ks/s will give you quite good copy.
I think the sampling rate depends on the "tolerable aliasing", "tolerable distortion" and dynamic range of the ADC.
We can not advise him/her to take a sampling frequency and we do not know the specifications.