I picked Russia due to their threat to European unity. Their aggression towards Ukraine, a Euro friendly state, and their overall opposition to the EU and a united Europe would be reason enough, for me, for Eurostar to look east. You could also argue that Eurostar would look at Russia as some kind of unwanted mongrel state due to it spanning the whole of Eurasia.
Regarding Eastern Europe, most of the states are either already members of the EU or are striving to be so I wouldn't see them causing too much damage there unless there was some political opposition in one of them.
Thinking about it more, if Brexit is involved in the game world, then absolutely I would expect attacks on the UK until they applied to rejoin. Since that would be seen as giving in to terrorist demands, I reckon you'd be looking at a long and sustained terrorist campaign against the UK and its assets around the world.
For cash, there's a whole wad of dodgy money in the Cayman Islands for them to steal. Maybe helping a corrupt Argentinian president in taking back the Falklands. Attacking members of the Commonwealth to pressure them to break away.
Regarding them trying to control Europe, I'd have them financing militant, extremist pro EU parties and trying to leverage them in to power, while attacking foreign assets. The end goal being the EU ran by leaders under Eurostar's control, essentially making the EU the political arm of Eurostar.