A B737-300 FLT CREW DEPARTING LAS LOADED AN INCORRECT RTE INTO THE FMC RESULTING IN THE WRONG SID BEING FLOWN.

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FIRST TIME WE HAVE FLOWN TOGETHER. FO HAD INADVERTENTLY PUT ENRTE TO BE LASONT VERSUS LASSJC (DEST WAS SJC) IN THE 'BOX.' I DID NOT CHK THE RTE AS I SHOULD HAVE. SO INSTEAD OF FLYING THE SHEAD DEP; WE GOT THE BOACH DEP. SHORTLY AFTER TKOF; FO (PF) ACTIVATED THE AUTOPLT AND LNAV AS PER PROCS. FLT OPS NORMAL UNTIL WE PASSED ROPPR. THE CORRECT COURSE AFTER THAT SHOULD HAVE BEEN 210 DEGS; BUT THE BOX HAD US FLYING 170 DEGS (AS PER THE BOACH SID). SHORTLY AFTER THAT; LAS DEP ASKED US ABOUT OUR RTE. I RESPONDED WE WANTED TO GO DIRECTLY TO SHEAD. HE KIDDINGLY RESPONDED BY SAYING HE THOUGHT WE WANTED TO GO TO LAX. I APOLOGIZED FOR THE CONFUSION AND HE CLRED US DIRECT TO SHEAD. ONCE AIRBORNE; I LOOKED AT THE RTE IN THE BOX; BUT NEITHER OF US REALIZED WE WERE FLYING THE WRONG SID. REMAINDER OF FLT WAS UNEVENTFUL. I HAVE NO EXCUSE FOR NOT CHKING THE RTE ON THE GND AND NOT REALIZING IT UNTIL IT WAS TOO LATE. I USUALLY CHK THAT RTE; BUT OF COURSE; THE ONE TIME I DON'T; IT BITES ME. ALSO; BEFORE DEP. I GOT A LITTLE BUSY (BUT NOT ENOUGH TO HAVE A VALID EXCUSE) COORDINATING FLT ATTENDANT'S REQUESTS AND GETTING CURRENT PAPERWORK. LESSON LEARNED: ALWAYS CHK THE RTE; REGARDLESS OF HOW BUSY IT WAS BEFORE DEP. I ALSO THINK THAT I WAS COMPLACENT AS I SHOULD HAVE NOTICED THE DISCREPANCY FROM THE SID IN FRONT OF ME VERSUS THE RTE PAGE IN THE BOX. SUPPLEMENTAL INFO FROM ACN 702169: DAY #4 OF 5 DAYS OF RESERVE. I HAD JUST FINISHED WITH A 3 DAY TRIP WHEN I HAD AN ADD-ON GIVEN TO ME OVER THE PHONE FROM SCHEDULING. I GOT TO THE JET PRIOR TO THE CAPT AND STARTED MY PREFLT. THE RELEASE WAS NOT AVAILABLE YET SO I LOADED THE FLT PLAN WITH THE INTENTION OF CHKING IT WITH THE RELEASE WHEN IT ARRIVED. I LOADED LASONT; WHEN THE CORRECT FLT PLAN SHOULD HAVE BEEN LASSJC. THE RELEASE ARRIVED ABOUT 20 MINS BEFORE PUSH. THE CAPT AND I TALKED ABOUT THE ROUTING; WX; NOTAMS; REJECTS; AND WHAT TO DO IF WE LOST AN ENG; HOWEVER; WE DID NOT CHK THE ROUTING IN THE BOX. WE TOOK OFF ON A NORMAL LNAV DEP WITH THE AUTOPLT ENGAGED; AFTER SETTING CLB PWR I BROUGHT THE LEGS PAGE UP AND FOLLOWED ALONG WITH MY CHART PAGE. I HAD THE SHEAD 4 DEP OUT WHICH IS WHAT OUR CLRNC WAS; THE BOACH 2 WAS IN THE BOX. THE FIRST 2 POINTS ARE THE SAME. WE GOT CLRNC TO CLB ABOVE 7000 FT SO I REFED THE CLB PAGE TO SET MY CLB PWR. AT THAT TIME WE STARTED A TURN TO 170 DEG HDG FOR RODDD WHEN WE SHOULD HAVE TURNED TO 210 DEG HDG FOR MDDOG. THE CTLR CALLED AND CLRED US DIRECT TO SHEAD AND THEN ASKED WHERE WE WERE GOING. WE APOLOGIZED AND SAID WE HAD THE WRONG DEP LOADED AND CONFIRMED OUR CLRNC DIRECT TO SHEAD. WE CORRECTED THE FLT PLAN AND THE REST OF THE FLT WAS UNEVENTFUL. BOTH PLTS SHOULD HAVE CHKED THE ROUTING IN THE BOX WITH THE CLRNC. COPIES OF SCHEDULING ADD-ONS WHILE ON RESERVE AWAY FROM HOME STATION COULD HAVE HELPED. HAVING 2 CDU'S WOULD ALSO HELP WITH SITUATIONAL AWARENESS SO YOU COULD KEEP YOUR ROUTING UP AND USE THE OTHER TO REF OTHER DATA SUCH AS CLB THRUST SETTINGS.