These are the trains we used to make up our Trans-Mongolian Journey. We decided to make a number of stops so we could see a variety of Russian and Siberian cities, and this probably increased the price somewhat. When we were booking the tickets Russian Railways was having a sale so our Kupe tickets were the same price as Platskarny. We booked most our tickets through Real Russia, which adds a service fee (about 10-15% the ticket price in my experience) but is really easy to use. Back when I was booking the tickets it would have taken 10 times as long, even now it take twice as long, and the site won't take our credit cards. For the Irkutsk to Ulan Ude leg I took a note up to the ticket counter with the details of the tickets I wanted, written in my little kid cyrillic and it worked! I'm relieved we didn't decide to do that for all the tickets though, even if it would have saved money. In all, the travel part of our Trans-Siberian came in at just under $800 each.
General Russian train info:
Typically the lower the train number, the better the train. Some trains also have names like the 002 "Rossiya"which makes the full journey from Moscow to Vladivostok. Some trains may have designations like firmeny (cleaner, newer cars, better services), or fast (really is just faster, not exactly fast)
Spalny Vagon is 1st class, 2 berths in one locked compartment
Kupe is 2nd class, 4 berths in one locked compartment.
Platskarny is 3rd class, 54 berths in one open cabin, arranged in bays of 6
(all times are local)
Kiev - Moscow 006 Dep Oct 16 at 19:14, arr October 17 at 09:01, Platskarny 13hrs
Moscow - Nizhny Novgorod 020 "Vostok" Dep Oct 20 at 32:55, arr Oct 21 at 05:47, Kupe 6hrs
Nizhny Novgorod - Perm 092 Dep Oct 22 at 19:20, arr Oct 23 at 11:58, Kupe 16hrs
Perm - Tobolsk 110 Dep Oct 24 at 22:17, arr Oct 25 and 14:00, Kupe 16hrs
Tobolsk - Omsk 395 firme Dep Oct 26 at 01:37, arr Oct 26 at 15:03, Kupe 12hrs
Omsk - Tomsk 030 Dep Oct 26 at 19:02, arr Oct 27 at 09:24, Kupe 14hrs
Tomsk - Krasnoyarsk 647 Dep Oct 28 at 19:28, arr Oct 29 at 07:40, Kupe 12hrs
Krasnoyarsk - Irkutsk 044 Dep Oct 30 at 01:32, arr Oct 30 at 20:32, Kupe 18hrs
Irkutsk - Slyudyanka 072 Dep Oct 31 at 06:37, arr Oct 31 at 08:43, Platskarny 2hrs
Slyudyanka - Ulan Ude 340 Dep Oct 31 at 12:03, arr Oct 31 at 17:16, Platskarny 5hrs
Ulan Ude - Ulan Bator Bus Dep Nov 1 at 07:30, arr Nov 1 19:30, 12hrs (way cheaper, way faster)
Ulan Bator - Beijing 024 Dep Nov 08 at 07:15, arrive Nov 9 at 14:04, 1st Class 31hrs