Transportation: airport, train, bus, metro, taxi... You could find the introduction in detail on this column: https://www.travelchinaguide.com/cityguides/beijing/transportation/
In downtown area, it is suggested you take the metro as many as possible, which is fast and cheap, covering so many destinations.

The must in Beijing include: the Great Wall, the Forbidden City, the Summer Palace, the Temple of Heaven, Beijing Hutongs and Counrtyards... Please find a full list on this page: https://www.travelchinaguide.com/attraction/beijing/

On the other hand, read others' travelogs in Beijing will be very helpful for you to arrange the trip!