FA50 FLT CREW OVERSHOOTS LOC ON APCH INTO SLC RESULTING IN A TCAS TA AND ADDITIONAL VECTORS.

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WHILE FLYING THE BRIGHAM CITY ARR TO SLC; WE HAD SET UP FOR THE ILS RWY 34R. THIS SEEMS TO BE THE USUAL APCH FOR ACFT THAT UTILIZE THE E RAMP. WE WERE GIVEN THE ILS RWY 34L AND HAD TO QUICKLY TUNE IDENT THE NAVAIDS AND BRIEF THE APCH. WE WERE GIVEN A VECTOR OF L TURN (FROM DOWNWIND) 070 DEGS THEN A VECTOR OF 010 DEGS TO INTERCEPT AND CLRED FOR THE APCH. WE MUST HAVE BEEN VERY CLOSE TO THE COURSE FOR IT CAME 'ALIVE' VERY QUICKLY. AS THE PLT MONITORING; I HADN'T NOTICED THAT THE PF HADN'T SELECTED APCH ARM BUT INSTEAD WAS IN NAV. BEFORE HE COULD MANEUVER THE AIRPLANE TO A HDG OF 010 DEGS. THE AUTOPLT TOOK THE AIRPLANE OUT THE LOC AWAY FROM THE ARPT. THE PF PROMPTLY DISENGAGED THE AUTOPLT; INITIATED A GREATER THAN STANDARD RATE TURN TO RE-INTERCEPT THE LOC. I; AS PLT MONITORING; RADIOED APCH THAT WE WERE COMING AROUND TO RE-JOIN THE LOC AT ABOUT THE SAME TIME WE RECEIVED A TCAS TA ON THE PLANE NEXT TO US ON THE ILS RWY 34R. ATC GAVE US A DSCNT AND RECLRED US FOR THE ILS RWY 34L. I THINK THIS SITUATION COULD HAVE BEEN AVOIDED BY ASKING ATC WHICH APCH WE COULD RECEIVE INSTEAD OF GUESSING. AS PLT MONITORING GIVE BEARINGS AND DISTANCES TO THE PF OF FIXES ALONG THE LOC COURSE; AND DOUBLECHK BOTH PLTS' FLT DIRECTOR MODES; IT IS PART OF THE APCH CHKLIST. SUPPLEMENTAL INFO FROM ACN 691080: THE LATE CHANGE OF APCH TO ILS RWY 34L AND 2 TIGHT TURNS; THE SECOND ONE TO '010 DEGS CLRED FOR THE APCH' COMING TOO LATE TO INTERCEPT; WITH A SIMULTANEOUS APCH ON ILS RWY 34R CAUSED ME TO TURN AT A 45 DEG ANGLE OF BANK TO TRY AND INTERCEPT.