E145 ON VISUAL APCH LANDS ON WRONG RWY AT DCA.

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WE WERE CLRED FOR THE RIVER VISUAL 19 APCH INTO DCA. AS I WAS FLYING THE APCH; MY MAIN FOCUS WAS AVOIDING THE P56 PROHIBITED AIRSPACE. WHILE AVOIDING THAT; WE HAD WHAT WE THOUGHT WAS THE CORRECT RWY IN SIGHT. WE WERE SWITCHED TO TWR FREQ. UPON CHKING ON WITH TWR; WE WERE CLRED TO LAND IN RWY 19. I LINED UP FOR THE RWY; AND CONTINUED THE VISUAL APCH AND LANDED. AS WE TAXIED OFF THE RWY; WE WERE TOLD TO CROSS RWY 19 AND CONTACT GND CTL. AT THAT POINT WE REALIZED THAT WE HAD LANDED ON RWY 15 INSTEAD OF RWY 19. GND CTL CLRED US TO TAXI TO THE GATE AND ASKED IF WE KNEW WHAT HAPPENED ON LNDG. I TOLD HIM WE DID. THE CTLR THEN TOLD ME IT WAS NO PROB. MY CAPT ASKED THE CTLR IF WE NEEDED TO CONTACT ANYONE; AND THE CTLR SAID NO. AFTER REVIEWING THE SIT; I HAVE DETERMINED 3 CONTRIBUTING FACTORS TO MY MISTAKE. FIRST; BOTH MY CAPT AND I WERE UNFAMILIAR WITH THE ARPT HAVING NEVER BEEN THERE BEFORE. SECOND; WE WERE SO FOCUSED IN NOT VIOLATING THE PROHIBITED AIRSPACE THAT IT DISTR US SOMEWHAT FROM CHOOSING THE CORRECT RWY. FINALLY; I DID NOT BACK UP THE VISUAL APCH WITH AN INST. HAD I SET IN THE LOA 19 APCH; I PROBABLY WOULD HAVE REALIZED MY MISTAKE PRIOR TO LNDG.