I'm an Indian planning to visit Baltic countries and Kaliningrad with my wife. I will be traveling from Moscow.
What visas would we need to travel by train?
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Because you intend to visit the Baltic countries I have to assume that you've already applied and/or received your Schengen visa. In addition to that you will need to make sure that your Schengen visa is not single entry otherwise you will need to carefully manage your trip.
In addition to the Schengen visa for the Baltic countries on your journey by train from Moscow to Kaliningrad you will need to get a Belarus Transit Visa (B) because the train from Moscow to Kaliningrad (russian) goes through Belarus before it gets to Lithuania.