If you can do not go during the summer peak season. Siberia can get very hot and there are lots of inserts (especially around Lake Baikal). Go in late September for the fall colors, warm days and cool nights. If you want to see the stunning snow and ice scenes, go late December to January.
Accommodations are spartan by Western standards, make sure to get a first or second class ticket. You might want to do this trip with friends since the sleeper cars hold 2-4 people. Make sure to confirm sleeping births reservations for each section of the trip (and for the correct days), otherwise you might be out of luck...