ACFT ON APCH TO RWY 19 AT DCA LINES UP WITH WRONG RWY AND IS ALERTED BY DCA LCL CTLR.

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DCA IS A BUSY PLACE; AS WE ALL KNOW. APCHING THE ARPT; ATC CHANGED THE APCH TO BE USED 3 TIMES. WIND WAS A FACTOR AND THEY 'TURNED THE ARPT AROUND.' WHEN A NEW APCH WAS ASSIGNED; EVERY ACFT CLRED FOR THE APCH COULD NOT PICK UP THE SIGNAL. THEY WERE THEN TAKEN OFF OF THE APCH TO BE RE-VECTORED FOR THE LDA RWY 19 APCH. WE WERE SUBSEQUENTLY CLRED FOR THE SAME APCH. XING THE FINAL APCH FIX; I CHKED IN WITH THE TWR AND RECEIVED A CLRNC TO LAND ON RWY 19. THE FO WAS FLYING AND WAS TRACKING THE LDA COURSE PERFECTLY. AT MINIMUMS; I SAW THE RWY AT 12 O'CLOCK POS. WE WERE IN A SAFE POS TO LAND. THE TWR CALLED AND SAID IT LOOKED LIKE WE WERE LINED UP FOR RWY 15; NOT RWY 19. AFTER WE REALIZED OUR MISTAKE; THE TWR CALLED BACK AND ASKED IF WE WOULD LIKE TO LAND ON RWY 19 OR RWY 15. I IMMEDIATELY STATED RWY 15 AS IT WAS THE SAFEST OPTION. THE DCA TWR CTLR CLRED US TO LAND ON RWY 15 AND APPARENTLY HAD NO PROB WITH THE RWY CONFUSION (ON OUR PART). NOTHING ELSE WAS SAID; AND WE PROCEEDED TO THE GATE WITHOUT INCIDENT. WE COULD HAVE EXECUTED A GAR; BUT THAT MAY HAVE JUST MADE MORE WORK FOR ATC. THE RWY WAS CLR; WE WERE CLRED TO LAND AND I VERY QUICKLY CHKED THE RWY ANALYSIS (BEING THE PNF) TO ENSURE WE HAD AN ADEQUATE LNDG WT FOR RWY 15. IN FACT; WE WERE 5000 LBS UNDER OUR MAX LNDG WT FOR THAT RWY GIVEN THE ABOVE CONDITIONS. IF WE WERE NOT; A GAR WOULD HAVE ENSUED AND A LNDG ON RWY 19 WOULD HAVE OCCURRED. AS TO THE CAUSES LEADING UP TO THIS EVENT; I HAVE MANY. AS PLTS; WE NEED TIME TO 'SET UP' FOR AN APCH. WHILE WE ARE SETTING UP FOR AN APCH; WE ARE STILL TRAVELING OVER THE GND AT 200-250 MPH. CHANGING THE APCH TO BE USED REQUIRES RADIO TUNING; CREW BRIEFING AND ACFT CONFIGN CHANGES. IN DCA; RWY 19 HAS A RWY HEADING OF 186 DEGS. RWY 15 HAS A RWY HEADING OF 153 DEGS. THIS DIFFERENCE IS 33 DEGS. SHOULD NOT THIS APCH BE RECLASSIFIED AS A CIRCLING APCH ('A' APCH)? WHEN YOU FOLLOW THE LDA COURSE AND THE RWY YOU SEE IS NOT THE CORRECT RWY; SOMETHING IS WRONG. LET'S CHANGE THESE PROCS; OR AT THE VERY LEAST; PUT A VERY OBVIOUS NOTE ON THE APCH PLATE TO INDICATE THE RWY IS SEVERELY OFFSET FROM THE ELECTRONIC COURSE. WHEN WE SAW THE RWY 15; WE WERE TO THE L (NW) OF THE PENTAGON; BUT NOT BY MUCH. IN LIGHT OF CURRENT EVENTS; THIS MAKES ME UNCOMFORTABLE AS A PLT. WE SHOULD NOT BE PLACED IN THESE SITS. I WOULD LIKE TO COMMEND THE TWR CTLR AT DCA FOR HELPING US OUT AND MAKING US 'LEGAL TO LAND.' POTOMIC APCH ALSO DESERVES CREDIT FOR ADAPTING TO THE LACK OF NAVAIDS AND KEEPING EVERYBODY 'ON TRACK.' THE SYS WORKS; WE JUST NEED TO KEEP IMPROVING IT.