Last time I made the trip, I took 3 pairs of slacks, 3 shirts, 3 pairs of socks, 3 pairs of underwear, and a minimal amount of the necessary bathroom sundries for washing, shaving, oral care, deodorant, etc. I was going for 3 weeks, and simply washed the clothes I wore each day, and changed to another set for the next day. If you pack smart, you can get away with only a carry on. If you take more than one suitcase that you have to check at the airport, you will have to pay extra for the second suitcase, up to $100.00 or more US.
Make sure you also take a decent digital camera so you can document the places you've been and the people you've been with. If you aren't a professional photographer, don't go overboard and get some huge digital SLR that is going to bog you down. I've found that a Nikon CoolPix camera is small enough, light weight enough, and has enough options for it to be a good all around camera and it has pretty good resolution for a small digital camera.
Also, unless you are already a fluent speaker of Russian, take with you a small pocket Russian-English dictionary or a lightweight electronic translation machine. Before you go, learn some basics, such has "hello, please, thank you, how much, and where's the bathroom." You should also learn how to use the toilet squatting instead of sitting, not that you'll have to do that everywhere, but there are places where it might be handy knowledge.