Air carrier Captain reported lining up with the wrong runway during approach to DCA and subsequently conducting a go-around. Captain stated they were assigned the LDA Y RWY 19 approach but used the RNAV 19 approach for the second approach to provide better guidance.

Narrative

When coming into DCA we were assigned the LDA Y 19. There was weather along the route of flight. We briefed the approach and the fact that it was offset. When getting closer to DCA we got multiple vectors and were sent through the final course and back around. Eventually we were cleared for the approach. Due to a reroute we were tighter on fuel than we had originally planned for so I was a bit distracted watching that as well. Once cleared we flew the approach and when I got closer I saw the runway and turned the flight director off. At about 500 feet. Tower queried us where we were going because we were lined up with 15. We immediately went around. We came back in and requested the RNAV 19 this time to help give us better guidance. We landed safely on 19 after the go-around. Cause: Neither the First Officer (FO) or I had been to DCA before so being unfamiliar with the airport and the fact that it had been a long day full of schedule changes and sits; and the external distractions of weather and fuel concerns added to my lack of situational awareness.Suggestions: In the future when going to a new or unfamiliar airport I would double check to make sure I have a full idea of what the approach will look like and the airport diagram itself. I would also request an alternate from Dispatch going forward if the weather enroute looks bad to give us more fuel.