DC10-10 FLC; UNFAMILIAR WITH ARPT; BEGIN AN INCORRECT VISUAL APCH AND REQUIRE MISSED APCH; AND OVERSHOOT ALT.

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I WAS ARRIVING INTO DTW ON THE SPICA 2 ARR FOR RWY 21L. IT WAS VFR; VISUAL APCHS WERE IN PROGRESS; AND I WAS UNFAMILIAR WITH THE ARPT. AT APPROX 6-8 MI OUT AT 2100 FT; ON A HDG OF 250 DEGS; I CALLED THE FIELD IN SIGHT; BUT NOT THE RWY -- A MISTAKE I WILL NOT REPEAT. I BEGAN A TURN TO THE S AND A SLOW DSCNT TO 1800 FT. AT THAT TIME THE DTW APCH CTLR CALLED TO ADVISE THAT MY PRESENT HDG WOULD KEPT ME TOO FAR L (E) OF RWY 21R. AT ABOUT THE SAME TIME I SAW RWY 21L OUT THE R FRONT WINDOW. WE WERE GOING TO PASS TO THE E OF RWY 21L AND WERE TOO CLOSE IN TO MAKE A SAFE VISUAL LNDG. I ASKED FOR A GAR AND VECTORS FOR ANOTHER VISUAL. APCH GAVE ME PRESENT HDG (210 DEGS) AND A CLB TO 2000 FT. IN EXECUTING THE MISSED; I OVERSHOT THE 2000 FT BY 300-400 FT. THE CTLR CLRED ME TO 3000 FT. I WAS VECTORED AROUND AND MADE A NORMAL VISUAL APCH AND LNDG. THIS ALL HAPPENED BECAUSE I HAD THE ARPT IN SIGHT; BUT WAS MISTAKEN. IN ADDITION; THE VECTOR OF 250 DEGS WOULD HAVE TAKEN US TOO CLOSE (ALMOST DIRECTLY) TO THE ARPT. SIMULTANEOUS APCHS WERE IN PROGRESS TO RWY 21L&R. AS A RESULT; I TURNED TOO EARLY; TO AVOID OVERSHOOTING THE CTRLINE OF RWY 21L. THIS PUT ME TOO FAR E TO PICK UP THE RWY LIGHTS UNTIL I WAS TOO CLOSE IN. IT WAS ALSO CONFUSING WHEN THE CTLR REFERRED TO RWY 21R; WHEN WE WERE E OF RWY 21L. IN THE FUTURE I HAVE DECIDED THAT IT IS BETTER TO ASK FOR AN APCH UNLESS I HAVE THE RWY IN SIGHT; AND AM SURE IT IS THE CORRECT ONE.