Air carrier flight crew on approach reported receiving a low altitude alert by ATC.

Narrative

During preflight planning my First Officer and I noticed numerous Notams for our destination airport. These included the normal runway (XX) closed; many taxiways closed and the runway XY ILS out of service. Based on the VFR weather; the most likely approach would be a Visual backed up by the RNAV GPS for runway XY. This short second leg of the trip from ZZZ1 to ZZZ was out of a hub turn which was preceded by a long inbound flight from ZZZ2 with only 1 hour and 30 minutes between these two segments. Our flight was normal until we arrived in the vicinity of the ZZZ airport terminal area. Approach control gave us a vector and a clearance to descend to 3;000 feet MSL. Then ATC asked if we had the airport in sight. A short time later; we finally made visual contact with the airport beacon. At this time; we were approximately 8 NM northwest of the field when we called the airport in sight. After receiving the Visual Approach clearance for runway XY from the controller; he had us switch frequencies to ZZZ Tower. As pilot flying; I immediately turned toward the RNAV final approach course and began a descent to 2400 feet MSL; which was the charted altitude for the FAF. Then I called for Gear Down; Flaps 20 degrees and the before landing checklist. As the aircraft approached the inbound course; I did my arrival check procedure. Then I noticed the aircraft not intercepting the RNAV inbound course; so I disconnected the autopilot and adjusted the heading manually to intercept. After this I got distracted trying to analyze why the course did not capture. During this preoccupation; I allowed the aircraft to descend to an altitude of approximately 1700 feet MSL (1000 feet AGL); while steering the aircraft towards the extended centerline of the runway. At this point; 4 NM out from the airport; I realized the aircraft was below the normal glide path since the PAPI lights were still red. Just as I started to stop the descent and level the altitude; the Control Tower reported a Low Altitude Alert for our aircraft. The remainder of the flight was uneventful. After extending the flaps to 30 degrees; I maintained this altitude until the aircraft intercepted the normal 3 degree glide path for the PAPI until touchdown on the runway.Forgetting to put the appropriate course tail extension on the Final Approach Fix; so that this proper point was sequenced in the FMS and allow the inbound course to be captured by LNAV. And not prioritizing the primary tasks of Aviate first then Navigate second. Also not requesting a vector to join the inbound course further out from the airport to add more time and avoid a rushed approach when mistakes are more likely to occur.Remembering to put the appropriate course tail on an RNAV fix while being radar vectored onto a Non Precision Approach by ATC so the correct course captures by LNAV. As pilot flying; not allowing any distractions to preoccupy my time and divert my attention away from the primary duty of flying the aircraft first. As a technique; requesting a vector to join the final approach course further out from the airport to add more time for task completion and avoid potential mistakes due to rushing.