I use two keyboard layouts (input sources) in my everyday work - the standard US and Russian-PC. In System Preferences/Language & Text/Input Sources I have activated the "Allow different input source for each document" option. Incidentally, I also have English as the top language in System Pereferences/Language & Text/Languages, even though that is not relevant to this particular problem. I also have Input Menu enabled at login window and experience no problems with that.
However, when launching a new window or application, I can never be sure what language I will start typing in. That's very inconvenient, especially in full-screen apps/windows/modes. I have been unable to determine a consistent pattern of when and why the input source changes or whether it even consistently "sticks" to the an application or window.
Extensive googling and searching through existing q&a here yielded no satisfactory answers. Most confuse the question with the language selection. I have once stumbled on a tip saying that if you press-and-hold the input source switch keyboard shortcut (Cmd-Space in my case), you will get a visual switch cue (which is true), and that the default will "stick" to the value at which you release the keys (which I couldn't prove is working, at least for me, also default for what? current window?)
So the question is - how do I set a systemwide default input source, which will be applied to every new invoked application and its windows?