SMA DEPARTS WRONG RWY DUE TAXI ON WRONG TAXIWAY. CITES POOR SIGNS; LIGHTING AT CLE.

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A RWY INCURSION TOOK PLACE FOR WHICH I WAS A PART OF. WE GOT OUR CLRNC AND BEGAN OUR TAXI INSTRUCTIONS WHICH WERE TO TAXI TO RWY 23L. WE PULLED OUT OF THE GA AREA AND TAXIED NBOUND ON J. WE KEPT TRACK OF OUR POS BY USING OUR ARPT DIAGRAM AND FOLLOWING THE TAXIWAYS WE WERE XING. A SMALL COMMUTER TURBOPROP WAS INSTRUCTED TO FOLLOW US TO 23L FOR TKOF. AS WE APCHED S THE TWR ASKED US IF WE WOULD BE READY FOR IMMEDIATE TKOF. I TOLD THEM A 2-3 MIN WAIT. THEY HAD THE COMMUTER TFC CONTINUE ONTO L AND WE WERE PULLED OFF J AND PUT ON THE RAMP AREA PAST TANGO INTXN. WHEN WE WERE CLRED FOR TKOF; WE CONTINUED FORWARD TURNED L ON WHAT WE THOUGHT WAS 23L. IN ACTUALITY WE TAXIED ONTO RWY 28 AND DEPARTED. TWR INFORMED US AT ABOUT 600 FT AGL WHAT WE HAD DONE AND GAVE US AN ON COURSE HDG OF 180 DEG. I BELIEVE THERE WERE A FEW FACTORS WHICH LEAD TO THIS RWY INCURSION. THE FIRST BEING THAT WE WERE TRYING TO EXPEDITE OUR RUNUP TIME TO PREVENT ANY BACK-UP FOR THE TWR. THE TAXIWAY IDENT SIGNS AND THE RWY IDENT SIGNS ARE VERY POOR IN THE AREA WE WERE IN AND DIRECTED TO ENTER ONTO RWY 23L. SECONDLY; I DID A POOR JOB OF KEEPING TRACK OF OUR EXACT POS IN RELATION TO THE TKOF RWY. A CAREFUL EXAMINATION OF THE RWY SURFACE AND DG PRIOR TO THE TKOF ROLL WOULD HAVE TOLD ME WE WERE ENTERING ONTO AND TAKING OFF THE WRONG RWY. I BELIEVE A LITTLE BETTER SITUATIONAL AWARENESS AND BETTER TAXIWAY AND RWY SIGNS MAY HAVE PREVENTED THIS FROM OCCURRING. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO. THE AREA IS VERY POORLY MARKED AND/OR LIGHTED. NO MATTER WHERE HE TURNED BACK TOWARD RWY; HE HAD TO CROSS 28 PRIOR TO REACHING 23L. TWR WAS NOT BUSY BUT GAVE NO ASSISTANCE OR GUIDANCE UNTIL AFTER THE FACT. TAXIWAY MARKINGS NEED IMPROVEMENT; LIGHTED RWY SIGNS WOULD HELP.