B737-300 FLT CREW HAS A HDG TRACK DEV DURING APCH TO DEN; RECEIVES A TCAS RA; EXECUTES A GAR AND RETURNS FOR LNDG.

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RWY 35L; CLRED FOR VISUAL APCH. RIGHT ABOUT THE TIME WE SHOULD HAVE STARTED THE TURN TO FINAL; THERE WAS A TA AT OUR 8 O'CLOCK POS; NO FACTOR; PROBABLY GOING TO RWY 34; BUT WE DID NOT SEE THE TFC. DISTR BY THE TA; TURN TO FINAL NOT INITIATED; AND THE AUTOPLT DID NOT CAPTURE. I DON'T KNOW WHAT AUTOPLT MODE THE CAPT HAD SELECTED; BUT I KNOW THE ILS FREQ WAS DIALED IN; NAV MODE VOR/ILS; VOR/LOC ARMED; AND FLT DIRECTOR OFF. HAVEN'T FLOWN THE -300 IN 5 YRS; SO I'M A LITTLE RUSTY ON SOME OF THE PROBS; BUT I REMEMBER THE CAPT AND FO SETTING UP THE FLT AND NAV INSTS FOR THE APCH AND ARMING VOR/LOC. I SAW THE OVERSHOOT DEVELOP; BUT HELD MY TONGUE FOR A SECOND. WE THEN GOT A 'DSND' RA; LOOKED OUT THE FRONT WINDOW AND SAW AN MD-XX AHEAD; ON FINAL TO RWY 35R. I LOOKED L; SAW OUR OVERSHOOT; AND TOLD THE CAPT TO TURN TO FINAL. AS HE INITIATED THE TURN; WE GOT A CALL FROM TWR ABOUT THE SITUATION. WE PASSED DIRECTLY AT 6 O'CLOCK POS TO THE MD; PROBABLY AT 1/2 MI AND SLIGHTLY BELOW. WE CORRECT TO FINAL AND CONTINUED THE APCH. WENT AROUND DUE TO LNDG WT AFTER ALL THIS; AND LANDED ON SECOND ATTEMPT. CONTRIBUTING FACTORS: 1) COMPANY QUICK TURN POLICY. QUICK TURN LNDG WT CALCULATIONS AND FUEL CONCERNS WERE INITIAL DISTR DURING CRUISE AND DSCNT. WE GOT A LOWER ALT; FLEW WITH SB EXTENDED; LOWERED GEAR EARLY; ETC; TO BURN FUEL. STILL HAD TO GO AROUND SO THEY COULD QUICK TURN THE AIRPLANE. IN THE FINAL ANALYSIS; THE FO HAD MIXED UP 2 LINES ON THEIR NOTEPAD PERFORMANCE COMPUTER; MISTAKING LNDG RWY 34R FOR RWY 35R. I CAUGHT THIS AFTER THE GAR AS WE WERE NEGOTIATING FOR A NEW LNDG RWY; STILL BASED ON THE QUICK TURN WT. NOT A DIRECT FACTOR IN THE TA/RA; BUT THE LNDG WT ISSUE DID USE UP A FEW EXTRA BRAIN CELLS. 2) UNFAMILIARITY OF CREW WITH DEN ALSO SEEMED TO BE A PLAYER. 3) DISTR FROM THE TA AT A CRITICAL MOMENT CAUSED THE INITIAL OVERSHOOT. 4) CRM WITH JUMPSEATER. I WAS THE FIRST TO CATCH THE OVERSHOOT AND ANOTHER DISTR; AND IT WAS TOO LATE. SUPPLEMENTAL INFO FROM ACN 701160: THE TFC ALERT IMMEDIATELY BECAME A TCAS DSND AND WE COMPLIED. AFTER WE ACQUIRED THE ACFT WE CORRECTED BACK TO FINAL RWY 35L. NEITHER OF THESE ACFT HAD BEEN CALLED TO OUR ATTN BY APCH CTL. THE 2 TFC ALERTS JUST AS WE WERE AT THE TURN TO INTERCEPT FINAL; WITHOUT KNOWING WHERE THE ACFT WERE GOING; WAS DISCONCERTING.