Types and regulation schemes LDOs
It sounds like you've got a solid understanding of control loop theory, and this is certainly something that needs to be addressed in the design. In my opinion, however, with and LDO regulator this is secondary concern.
With over 20 years experience as a professional EE, here's my process for choosing an LDO for an application...


Find a device that provides the required load voltage and current with the given input voltage. With an LDO, the load current the device can supply should be de-rated by at least 20%.
Perform a thorough thermal analysis, where the LDO is operating at maximum load current at the maximum input voltage at the maximum ambient temperature. Consideration needs to be given to the type of heat-sink being used and the sum of the thermal impedances to ensure that the junction temperature of the device never exceeds the max allowed. If a device cannot be found that will operate comfortably under these conditions, it's time to consider a switching supply.
Now, follow the datasheet regarding the input and output capacitor requirements. If the capacitor manufacturer doesn't provide information regarding ESR, use an LCR meter to measure the ESR of the capacitors.