AN E145 CREW; ARRIVING LBB; IN WX; HAVING EXPERIENCED NUMEROUS RWY CHANGES; EXECUTED A GAR WHEN APCH BECAME QUESTIONABLE.

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BOTH FLC MEMBERS FATIGUED. WE WERE IN THE 11TH HR OF A 13 HR DUTY DAY. ENRTE DEVS FOR TSTMS WERE A FACTOR ALL DAY LONG. FLT WAS SCHEDULED TO BE FROM ZZZ TO LBB. APCHING THE LBB AREA; ATIS WAS APPROX 7 SCATTERED; 12 BROKEN; 3 MI VISIBILITY; WIND 080 DEGS; AT 12 KTS. TOLD TO EXPECT AND CREW BRIEFED ILS RWY 17R. WHILE AT 5000 FT; ATC ANNOUNCED RWY LIGHTS FOR RWY 17R JUST WENT OTS. (FO WAS FLYING.) ATC TOLD US TO PLAN FOR VOR-DME RWY 8. WE XFERRED CTLS AND FO BRIEFS THE APCH. WE XFER CTLS BACK. I CONSULT THE APCH PLATE AND REALIZE THAT THIS IS IN FACT AN RNAV APCH; NOT APPROVED IN OUR OPS SPECS. ATC; AFTER BEING SO INFORMED; NOW SUGGESTS VOR A APCH. WE AGAIN XFER CTLS; REBRIEF; AND XFER BACK. FATIGUE; FEELINGS OF BEING RUSHED; ETC (FUEL CONCERNS) ARE FACTORS IN THE COCKPIT. WX NOW RPTED AT 1000 FT; 3 MI; WINDS 080 DEGS AT APPROX 20 KTS. AN ACR IN FRONT OF US RPTS A MISSED APCH (RAIN SHOWERS IN THE AREA). THE FO DOES NOT FLY A VERY GOOD APCH AND I CALL FOR HIM TO EXECUTE A MISSED APCH PRIOR TO THE MISSED APCH. AS WE FLY OVER THE ARPT AND FOR A TIME AFTERWARDS; I CAN SEE THE RWY AND WHEN ATC SUGGESTS THE ILS RWY 17R CIRCLE TO LAND RWY 8; THIS SOUND LIKE A GOOD IDEA. WE PREPARE FOR ANOTHER APCH. ONCE AGAIN; THE FO STRUGGLES WITH THIS APCH. WE BREAK OUT OF THE CLOUDS WITH THE ARPT IN SIGHT AND BEGIN THE CIRCLING MANEUVER. THE WIND IS NOW VERY STRONG OUT OF THE E. AS WE CIRCLE AND DSND TOWARDS RWY 8; THE BANK ANGLE; RATE OF DSCNT; ETC; BECOME SUCH THAT; IN MY OPINION; THE SAFETY OF THE FLT IS IN DOUBT. I TAKE THE CTLS AND LAND THE ACFT. MANY MISTAKES WERE MADE ON THIS FLT IN ADDITION TO PURE STICK AND RUDDER FLYING. PREFLT AND INFLT PLANNING AND DECISION MAKING ARE FOREMOST. WE SHOULD HAVE DIVERTED TO THE ALTERNATE. THOUGH I BLAME MYSELF FOR THESE ERRORS; I BELIEVE THAT FATIGUE PLAYED A STRONG ROLE.