Air carrier Captain reported conducting a go-around following an unstable approach. During the second approach attempt the flight crew received a caution obstacle" alert."

Narrative

Flying into DCA at night; we were clear to fly the visual river approach to RW 19. For me (Captain PM);it was the second time flying this approach; but first time at night; and first time as CA. We planned to configure early so that we could focus our attention to the final segment of the approach and avoid P-56 while flying a visual to the airport. We had an inoperative MFD on the FO (First Officer) side and MEL required PM duties to working MFD side (in this case CA side). At some point while descending on the visual; speed started to increase and I advised PF to watch the speed" and FO immediately corrected; we never exceeded any limitations. We continued down looking for the airport environment and runway but when we finally identified the runway; we were high and not in a position to continue the approach; at that point we decided to go around. We were instructed to fly heading 250 and climb to 3000 ft. We were given vectors around for a second try. Again; we were cleared for the same approach; River visual RW 19; configured the aircraft; and this time we flew a little closer to the west side of the river to again avoid P-56. We continued descending; looking for the runway; this time ATC asked if we wanted/could take RW 15 since we were already aligned with it; and at that point we accepted. We were given a clearance to land on RW 15; we had the numbers for both runways; so we landed on RW 15. At 500 ft; CA took control of the aircraft and had an uneventful landing and taxied to the gate. Landing weight was below 62000 pounds so we had a safe margin for any runway. While descending the second time; we got a bit closer to obstacles; we had them in sight at all the times but "caution obstacle" alert was activated. Both FO and CA had limited experience flying into DCA. First time for CA flying this approach at night and same for FO. Before we departed ZZZ to DCA; both crew members reviewed the training material provided on the airport section of company material and also studied the Jeppesen pages for DCA; however; the complexity of flying this approach at night and the limited experienced was the main factor for this event. This was CA 3rd time into DCA. Inoperative MFD on PF side. I would suggest to let new Captains fly into DCA with a LCA (Line Check Airman) at least twice and at least once at night. I strongly suggest a training video like the one we have in ZZZ1."