The Trans-Siberian is a dream of mine too.  In college I studied Russian as a language, and in more recent years I have studied Mandarin.  While my skills are barely sufficient to order a beer, it would still be fun.

I thought that I read that to do it properly, the trans-Siberian takes more than a week.  Ideally you would get off at various points and see some of the cities along the way.  Sitting on a train for a week solid could get a little old.

You have your choice of whether you end up in Beijing or in Harbin.  I have been to Beijing already, but a lot has changed since I was last there.

http://www.seat61.com/Trans-Siberian-timetable.htm