Beijing Loop

I know there are three popular train routes that include China. I am trying to get information about Beijing going north through Changchun, Harbin and Manzhouli into Russia where I can take another ride from Chita into Mongolia and back to Beijing. It is proving somewhat confusing. Are tickets purchased at each station I hope to stop in, or can I pre-book if I know how long I will be in each city I plan to visit? Is it possible to stop along the way once in Russia and Ulaan Baatar? I do not want to just sit on the train the whole time.
Thank you!