What happens when an update to a steam game comes out while Im downloading this game?

Let's say I'm downloading a game over night and in the middle of a night, during downloading, new update to this game comes out. What happens ? Does my download stop ? Does it download but later I have the game in an old version without this update ? Or does the update download for me once the initial downloading of the game is finished and everything is fine after that - my game works properly in the latest version like everyone else's ?

Last I checked your download will continue even though a new version is available. The next update will be queued after it and it should go automatically, as long as you haven't restricted automatic updates in the Steam Downloads settings.