There are tons of travel agencies offer tours to the great wall. Great Wall Tour, Beijing Great Wall Tour - Beijing Great Wall. Most popular is Badaling. You will have nice weather in September.
Airport is not far away. Just go to the taxistand, be sure they turn on the taxi meter. To the center will be around 120 RMB (Yuan). And try to print out the hotel name in chinese and show it to the driver.
Do not miss the Silk market! You will get the info by asking your hotel concierge. They usually have card of the hotel for the taxi driver, on the back there are the hotspots of beijing described.