B737-300 CREW AT CLE MAY HAVE MISUNDERSTOOD THE CTLR'S INSTRUCTIONS WHEN TOLD TO CROSS RWY 24L AND INTO POS ON RWY 24C.

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CLE'S RWY LAYOUT AT THE APCH END OF RWY 24L IS CONFUSING AT BEST; AND WAS WORSENED IN OUR SIT WHERE THE TWR CTLR CLRED US INTO POS ON RWY 24C WHILE ANOTHER ACFT WAS ON A 2 MI FINAL. ACFT AWAITING TKOF ON RWY 24C ARE REQUIRED TO TAXI ON RWY 28 AND EVENTUALLY CROSS RWY 24L TO GET THERE. ANOTHER ACFT WAS HOLDING IN POS ON RWY 24C. WE WERE CLRED TO 'CROSS RWY 24L; TAXI INTO POS AND HOLD ON RWY 24C.' UNFORTUNATELY; THE CTLR CLRED THE ACFT HOLDING ON RWY 24C FOR TKOF AFTER HE CLRED US TO TAXI INTO POS ON RWY 24C. WE STARTED ACROSS RWY 24L AND REALIZED THIS WOULDN'T WORK BECAUSE THE PREVIOUS ACFT HADN'T STARTED MOVING. WE WERE FORCED TO STOP ON RWY 24L. THE AIRPLANE ON A 2 MI FINAL WAS NOW ABOUT 1 MI AND WAS TOLD TO GO AROUND BY THE CTLR. AT NO TIME WAS THERE ANY DANGER OF A COLLISION; BUT THE AIRPLANE HOLDING ON RWY 24C SHOULD'VE BEEN CLRED FOR TKOF FIRST. IN THE FUTURE; I WILL HESITATE TO START MY TAXI INTO POS UNTIL THE ACFT AHEAD BEGINS TO MOVE. COMPLICATING MATTERS WAS THE FACT THAT THE AIRPLANE ON FINAL (A B737) WAS FAIRLY CLOSE IN; AND WE HAD TO MOVE QUICKLY TO MAKE THINGS WORK OUT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED TAXIING AT CLE ARPT IS VERY CONFUSING BECAUSE OF THE CONSTRUCTION IN PROGRESS. WHEN ASKED IF THE CTLR EXPECTED THEM TO TAXI AROUND THE APCH END TO RWY 24C; THE RPTR SAID THEY SHOULD HAVE REFERRED TO THE ARPT CHART BEFORE TAXIING. HE SAID HE NOW UNDERSTANDS WHY THE CTLR ISSUED A CLRNC TO CROSS RWY 24L AND TAXI INTO POS AND HOLD ON RWY 24C.