CRJ700 Captain reported failure to comply with company procedure resulted in a terrain caution alert and a CFTT event during approach.

Narrative

Coming into ZZZ on the evening of Day 0 the FO was PF and was told to descend to 3000 feet to join a right downwind for a visual approach Runway XX. Once level at 3000 we were given a visual approach clearance. The FO did a great job of extending downwind a bit and turned base outside of the FAF. He asked me if we were clear of all obstacles to descend to the FAF altitude of 2600. After double checking I told him he could square it up and there were no obstacles in the way so we would be safe at that height. I did mention the tower outside the FAF at 1300 feet but figured because we would be level at 2600 it should not cause an alarm. I was completely wrong about that and we received a terrain caution to which I immediately called go around. The FO began performing a go around and then I took controls stating my controls." I went a little more aggressive smashing thrust full forward and calling for "set max thrust and check spoilers." I knew previously that we were at a safe altitude; however; I didn't want to take any chances so I immediately got the plane to 4000 feet. At that point I advised him to tell Tower we were going around and to get a heading. Tower asked why we went around and told us that we were at a safe altitude to conduct the approach. We acknowledged we thought the same; but had to respond to the aircraft's alerting system. He then gave us a heading to come back around to join the ILS XX. Once we got configured again with the autopilot on I gave the controls back to the FO so I could call the FA's (Flight Attendant) and make sure they were ok as well as update them as to what happened. I made a quick PA to the passengers letting them know everything was ok we had to box around and we would be conducting the approach again safely momentarily.Based on my experience in ZZZ over the years I should have known to have him straight fly the ILS based on mountainous terrain at night; however my judgement was lacking and I felt perfectly safe with the approach. 100% my fault for not being a better PIC and requiring an ILS as well as not talking about the altitudes better on the company pages that explains this very scenario in depth. We had reviewed the page earlier; however I remembered it wrong as being 3000 outside the final approach fix to avoid the terrain caution. When Tower gave us the altitude of 3000 and we reviewed again all the obstacles in the area we felt perfectly fine to shoot the approach. I take full responsibility for the event and commend the FO for a job well done under pressure."