How to compensate an op-amp at a particular frequency?
If an amplifier is inadequately compensated it may oscillate even with no input signal applied.

Plot loop gain (open loop and feedback network combined) and phase and adjust the compensation capacitor's value to make sure that the loop gain gets down below 1 well before the loop phase reaches -180 degrees, (say 50 degrees before.) This should then give stability when the loop is subsequently closed.

Usually such a high value of closed loop gain would give you a big advantage of being able to compensate for a high bandwidth. (With a lower beta open loop gain can be higher giving increased bandwidth).  But high bandwidth is not important to you. So with a beta of 1/100 you can compensate for an unusually high phase margin giving very good stability and not worry about the reduced bandwidth that results.

But bear in mind that the bigger the required phase margin, the lower the open loop gain will need to be (for any particular beta) and the lower the feedback factor (1 + B.Aol) will be resulting in reduced performance such as higher distortion levels.

So it is a compromise between stability and performance. 

beta, B = 1/(Noise Gain)