I see you guys are planning on taking the train from Beijing to Moscow. In October of last year, we took it going the other way, and had a fantastic time. We stopped in Irkutsk, and spent a few days in a tiny town about an hour outside called Listavyanka. It wasn't touristy, we stayed in a homestay (where the owner of the house puts you up as a guest & feeds you whatever the family are eating) and those few days really stood out as a highlight of a yearlong trip. 

As for the train journey itself, I can't stress enough that you bring a lot of books and instant coffee. And vodka. Do promise that you'll be careful with the vodka, otherwise, you'll end up drinking your entire supply for 4 days in one evening, and then there'll be vomiting, and that just makes everyone uncomfortable. 

The cabins come in 2 or 4 berth flavours. We were travelling in a group of 4, and got a cabin to ourselves, but then we made friends with the 2 swedish guys in the next cabin, and they had their 4 berths to themselves for most of the journey, so it's the luck of the draw, i suppose.