Hi! My family is visiting great wall for 1st time on january.

Well, Xicheng District refers to a large area, would you like to provide detailed starting point?
Anyway, you can take a bus or taxi to Dongzhimen, and there are two direct buses from Dongzhimen to the great wall at 10:00 and 12:00. If you miss the bus, still at Dongzhimen take the bus No. 916 to Huairou North Street. Then hire a car to the great wall at a cost of CNY50 around.

xicheng district is near to the Main Train station,but it is a little far from PEKING airport, i suggest you will take a formal taxi(not the privacy car) and according to the taxi's meter, if you may,you can choose the subway, the subway will deliver you to everywhere.

I think u can take a taxi. Through some software in Internet, u can get one. It is much cheaper than usual.