Hi, I have taken that trans-siberian when i was a kid in 1992.
My advice is know your starting point. Are you starting out in Mongolia, Russia, or China? What city? What do you want to see? Once you know where to start depending on the country specific problems can be solved easier. Generally, it is better to book the lux rooms because the regular ones were little too rough for a long travel.
I think you should carry smaller bills keep in case you have to pay for someone to do their jobs or buy nick nacks (sp?) along the way.
It is a beautiful to experience vast lands, culture and climate changes.
Good Luck,