A320 FLT CREW HAS MULTIPLE APCH/RWY CHANGES DURING ARR TO MMMX.

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FLIGHT WAS ROUTE QUAL TO MMMX; WITH LCA IN R SEAT AS PNF; AND CAPT IN L SEAT AS PF. THE ARRIVAL AND APPROACHES HAD BEEN THOROUGHLY BRIEFED; HAVING NOTED NOTAM 20/723 ILS RWY 05R FREQ 109.1 UNSERVICEABLE. WE HAD BRIEFED VOR DME-2 05L/R W/ SMO TRANS; THEN WHEN WERE TOLD TO EXPECT RWY 23L. WE REBRIEFED EXPECTING ILS DME-2 RWY 23L WITH OTU TRANS. WHEN ON VECTOR TO FINAL; DESCENDING TO 8700 FT; CONFIGURED TO F3; GEAR DOWN; WE WERE DIRECTED BY MMEX APCH INTERCEPT MEX 052 FOR VOR RWY 23L; WHICH WAS A SURPRISE; SO WE WERE TRYING TO GET SET UP FOR THIS VOR APCH NAV PROCEDURE. BEFORE WE COULD INTERCEPT FINAL; WE WERE DIRECTED TO CLIMB TO 11000 FT; FLY DIRECT SMO; RWY IN USE IS BEING CHANGED TO RWY 05L/R. WE WERE IMC; PF (CAPT) HAND FLYING WITH AUTOPLT AND AUTOTHROTTLES OFF AND INITIATED A NORMAL GO AROUND. CAPT QUICKLY GOT BEHIND THE AIRCRAFT; IE; I DID NOT GET NOSE UP TO 15 DEGREE TARGET AND WAS SLOW TO CALL FOR F2 AND GEAR UP. LCA SAVED A FLAP OVERSPD BY GETTING FLAPS TO 2; BUT WAS OVERLOADED BECAUSE OF MY POOR HAND-FLYING AND MULTIPLE ATC INSTRUCTIONS. WHEN ANSWERING MMEX APCH USING THE SIDESTICK MIC BUTTON/SWITCH; LCA MOMENTARILY MADE AN INADVERTENT CONTROL INPUT WHICH GAVE US THE DUAL INPUT VOICE ALERT. AUTOPLT AND AUTOTHROTTLES WERE REENGAGED AT THE LCA'S REQUEST AND WE GOT FURTHER MMEX APCH INSTRUCTIONS TO FLY HDG 230 TO INTERCEPT SMO 160 OUTBOUND FOR THE VOR DME-2 RWY 05R; AND DESCEND TO 9700 FT. WE CONFIGURED AND WERE THEN GIVEN A VECTOR TO INTERCEPT MEX 232 (FINAL APCH CSE) AND DESCEND TO 8800 FT. WE WERE ABLE TO SEE THE FIELD AND COMPLETED THE APPROACH IN VMC TO A LANDING ON RWY 05R. FACTORS WHICH MADE THIS SO EXCITING WERE MY DECISION TO HAND FLY WHILE ON VECTOR TO FINAL; MY POOR EXECUTION OF THE NORMAL GO AROUND RESULTING IN OVERLOADING THE PNF/LCA; ATC INSTRUCTIONS THAT WERE DIFFICULT TO UNDERSTAND COMPOUNDED BY BACKGROUND STATIC ON THE MMEX APCH FREQ; AND HIGH TERRAIN BETWEEN OUR POSITION AND SMO. ALSO; RELOADING THE FMGC BECAME PROBLEMATIC BECAUSE OF MULTIPLE FREQS ASSOCIATED WITH SMO VOR. WE REVERTED TO RAW DATA TO ENSURE TERRAIN CLEARANCE AND TO COMPLY WITH ATC CLEARANCE. LCA HAD DONE A GREAT JOB BRIEFING AND PREPARING ME FOR THE ARRIVAL; BUT I HAD NOT UNDERSTOOD WHAT HE MEANT CONCERNING AUTOPLT AND AUTOTHROTTLES USAGE; AND WHEN I DISENGAGED BOTH IT MADE FOR A VERY DIFFICULT SITUATION DURING THE GO AROUND. LCA THOROUGHLY DEBRIEFED THE EVENT WITH ME.