When I see how popular with foreign tourists the Trans-Siberian Railway is, I clearly understand how little they know about Russia and travel by train. To be honest, I've never travelled by the Trans-Siberian but I'll never ever do it because that's how I see it.
Russia beyond the Urals.
The main historical events of Russia took place in the European part of the country, hence, not further than the Urals. The Urals and Siberia were mostly the industrial regions where natural resources were exploited, some factories were situated but all the culture and most historical sights have always been in the European area (Moscow and Saint-Petersburg, towns of the Golden Ring of Russia).
What do travelers expect to see beyond the Urals? One has to be a thorough explorer of history in order to shortlist proper sights in that area to see. However, if you are into nature, you'll be able to see a lot but by not staying on the train. Travelling by train you're most likely to see the characteristic of Russia lots of plain areas with rows of half-destroyed unattractive log cabins (apparently most country citizens live in such houses), monotonous kilometers of dense forests and fields.
The attractive site there is the Chusovaya River but in order to see it you have to go rafting, and get off a train. Maybe horseback riding in Altai but, again, avoid the train. ))
You may also hope to see some Russian towns and enjoy tours of them. I wouldn't be so optimistic about it. Russian economy is in decline due to overwhelming corruption, flight of capital, overall poverty of Russians. That's only natural that nowadays most towns are degrading. Even the towns of the Golden Ring of Russia which I dearly love and laud in my blog for their unparalleled archaic atmosphere look rather poor, deserted, outdated in terms of ordinary people's life quality. Leave alone some ordinary industrial towns like those you'll see traveling by train in the remoteness from main cultural centers.
The train travel.
Have you actually travelled by train for more than 5-6 hours? I have. We used to travel a lot to Vyatka/Kirov, a town half-way to Ekaterinburg, to my granny's.
The journey takes around 30 hours, and even that was boring enough. After 14 hours on the train one feels his muscles ache a bit since you can't move and have even the minimum of normal amount of daily physical activity. The next day it's finding ways to fight boredom: watching tree trunks flashing by is no more fun)). It's also poor hygiene a traveller suffers from: the cars of Russian railway are sort of dusty, there's either no air conditioning or it's somehow deficient.
Well, I've just brought up the points they will never reveal to you at travel agents' or when you buy overpriced Trans-Siberian tours. It's up to you to decide. On the bright side, you'll certainly have a new exotic experience, see the true Russia without the gloss of tourist deceptive traps, feel the country's enormousness and make your dream come true (because you should really want it badly if you take the risk of going throughout all Russia by train).