Air carrier Captain reported unintentional aircraft movement after parking at the gate when parking brake was not set. The Captain recognized the unintended movement and quickly set the parking brake; and no injury or damage was reported.

Narrative

After taxing into the gate at ZZZ on (Day 0) and coming to a complete stop; I shut down the engines; I gave the all clear signal to the Marshaller. I then either attempted to set the brake and it did not engage; or I forgot to set the parking brake (I honestly cannot recall); and gave the parking brakes set signal to the Marshaller. I held the brakes until I thought I saw a chocks-in signal; took my feet off the brakes; the aircraft started to roll; and then I put my feet back on the brakes; stopped the aircraft from rolling; and realized the parking brake was not set. I then set the parking brake. The Ground Crew installed the chocks; the aircraft was still in a good position for the gate to approach and deplane; so we continued with our Parking Checklist and deplaned the aircraft as normal.During upgrade training; we were initially taught the parking/shutdown flow out of the AOM; which had us set the parking brake first. However; due to recent events that were happening with new/inexperienced Ramp Crew entering the Safety Zone; before the engines were shut down; some of the instructors placed an emphasis on getting the engines shut down first and/or as quickly as possible. So towards the end of training I changed my flow to shut the engines down first and then set the parking brake. I believe a number of factors contributed to the roll back. I believe my focus on shutting the engines down first contributed to either missing the parking brake or incorrectly setting the parking brake. I also believe there was a miscommunication between the Ramp and the Flight Deck as to whether the chocks were in or not. Ultimately; the responsibility falls on me; as the Captain; to make sure the AOM is followed and the aircraft parking brake is properly set. Since that event; I have gone back to setting the parking brake first; as the AOM clearly states. I don't anticipate any problems going forward; but I do believe our training should be looked at closer and a clear distinction made as to what step we should do first.