I've taken several overnight trains from Petersburg to Moscow. I was in a second class cabin, and even there I felt entirely safe. If you and your travelling partner are together in a first class cabin, you should be perfectly fine. You'll have the cabin all to yourself, so after your ticket and passport are checked by the train attendant, you can lock the door while you sleep. I haven't been on train #6, but it should be pretty nice -- the nicest Russian trains are numbers 1-10. Your beds will probably already be made up for you when you get on the train.
I have trouble sleeping on the Pete-Moscow train because it's not actually that long a train ride. It's barely even seven hours, and since it takes a little while to show your ticket and get yourself all situated and sleepy, there isn't quite a full night left for sleeping. I think the beds on Russian trains are very comfortable--they're quite large, although perhaps a little bit hard. Your train car will have an attendant assigned to looking after the guests on just your car. They can be a little bit surly, but are generally rather helpful--she may ask you if you want to buy some cheap snacks, tea, or instant coffee. There is a hot water samovar at the end of the car that you can help yourself to. The train attendant's room is usually across from this--if you have a problem, you can knock on her door and she is required to help you. She probably won't speak English though. Usually at the other end (or sometimes at both ends) is your bathroom. This is the only bad part of the train -- even in first class the bathroom probably won't be too nice. I would advise against sitting directly on the toilet seat. The bathroom in the train station in Moscow isn't much better, alas.
Have a great trip!
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