You need a confirmed onward ticket out of China on a flight which doesn't stop in China on the way. Your ticket must be to a third country, you can't go back to where your arriving flight left from even if it's only to catch a connecting flight. You have to leave from the same zone that you arrived in, which doesn't seem to be a problem. Carry your passport at all times when outside the hotel, you will need it for entry to certain attractions anyway. The procedure at Beijing is quite straight forward but allow a bit of extra time when you check in for the flight to China, and preferably print out the rules from the official website as check in staff may not be familiar with the procedures and will definitely go through a thorough check to cover themselves.
Read up on Beijing scams before you go, there are quite a few, especially the tea house and traditional medicine ones, otherwise enjoy your trip.