Visa for Russia is essential and probably the most expensive. If you’re American you probably get 90 days in Mongolia without a visa (I got 30, being Israeli). Make sure at you local consulate, and whatever you do- don’t overstay (I paid 135$US for one day. Expensive). Being American might cause you a bit of hassle with the Chinese visa- but you can’t have it all.
I took the No.4 train from Moscow to Beijing direct (that’s the Chinese one), and a sleeper, but not the deluxe. It was more then reasonable- and highly recommended. The ticket cost 250$US through a Russian agency, which was very reliable.
Next time I’ll take the train I’ll probably stop for a few days in Moscow, Irkudsk, and probably Omsk and Novosibirsk, and st. Petersburg, of I’m headed north. And be sure to take at least three weeks in Mongolia- an experience I’ll be glad to relive.
Tell me if you need any more info on the trip or on the agency- I’ll be glad to assist :)
asaf