It's common to travel by trains in Russia. To go to Belarus / Ukraine the best option is to take a night train to the border and cross the border by other transport / by hitch-hiking (crossing a border makes a train ticket cost 2 times more).
- Bus: Simple Express
Not sure if this is up to date, but some info here http://wiki.apnchanger.org/Russia
Apparently most places have free wifi in Russia, it's allegedly very common.
Russia has an extended system of bureaucracy.
Most nationals of Western countries require invitations for a visa to Russia. Most EU states can now (June 2014) obtain a visa without an invitation, but through a travel agency. For example, in Berlin this costs €85 (June 2014) for a German passport and €105 (June 2014) for a UK passport.
- Russian music thread on FB for inspiration