I default to the c-chart (which assumes a Poisson distribution) whenever I am counting events, defects, injuries. Most times (in my experience dealing with such data) each individual event is independent from each other. The closely related u chart also works well, for example, OSHA recordable injuries per 200,000 hours worked.
BUT in this case, the sum total of the complaint data showed a variation higher than the Poisson. Therefore, I tried the iMR chart (and probably woudl not be a bad idea to plot the R chart, but that usually ends up confusing folks more than enlightening them, IMO). Since it fit, I conclude that either there are "lumpings" of complaints (one initiating event begats multiple complaints), OR there is a mixture of different variations in the individual feeds. Thus, a good thing to do is start going down to the individual categories and sources of complaints to see what that tells you.
On the flow chart, I initially followed the "discrete data" path, then defects, then c-chart.