If travelling anywhere within Russia, use the train. The vast distances covered mean that all trains (apart from the local suburban ones) are sleeper trains. If you want privacy you can book a four or two berth cabin, but I recommend the third class (platzkartny) carriages – they are open with four berth alcoves, and are a great way to meet people. You could be sitting with all kinds of people, from babushkas taking their little grandkids on a trip, to young guys on their way to start their military service. Most train journeys are at least several hours long, so you will get to know your fellow passengers quite well, and it makes the journey much more interesting. Make sure you stock up on plenty of supplies for the journey, as much to share as for your own consumption, although there is often a restaurant car (quite good quality actually) and at most stops there are people selling all kinds of food and drink such as crisps, fruit, homemade meat cutlets, pierogi.