Anyway, the device you linked to seems a bit excessive since the main focus of that device appears to be making third party CT's act as a Lecroy current probe.
As previously stated startup current may be as high as 20 times running current so of running current is 125A you will probably have to be able to measure currents reaching a peak value of close to 2.5kA.
If we translate that to the 10 bit A/D-conversion maximum resolution will something like 2.5A
As for calculating burden resistor it's basically just Ohms law.
 I would suggest getting a cheap CT and hook it up to a burden resistor and an oscilloscope to get a better feel of the kind of signal you can expect. I used a schottky rectifier to get a DC signal to my arduino since my project did not require very high accuracy or resolution. With calibration it can still get quite decent.
Also , of course , if you are trying to protect a motor in this way ( as is previously said, not a great idea IMO) , you have to be able to measure and act on small over loads and also much larger fault currents ( as implied by other posters ) - so its a complex task and you need to speak to a CT manfacturer. You also need to look at the “ competition” - trips that attach to motor contractors that are co-ordinated with fuses ( and their overload characteristic - fuses, overload devices, contactors and the motor, and it’s duty cycle need to be co-ordinated together ) to provide good protection at a low price.
The secondary current is N times less than the current being measured for a CT with a turns-ratio of N
For example if a 1000:1 CT is measuring 50Arms with a burden resitor of 200 ohms,
the secondary current = 50/1000 = 0.05Arms.
power in burden resistor is I^2 * R = 0.05^2 * 200 = 0.5W (yes, watts, not VA, its a resistor so true power = apparent
And of course the voltage across the resistor is 0.05 * 200 = 10Vrms
Do you understand about rms, peak and peak-to-peak? That's vital for understanding
the limitations of sampling the CT output with an ADC.