What is the correct way to use to-infitives?

This topic often confuses me. Sometimes I am not even able to understand the meaning of a sentence. For instance, the sentence:

"White to move".

You can hear it in chess, it means that the player with white pieces has to make his turn. Unfortunately, I couldn't find the rule to explain this expression.

"My first movie to watch was ..."

Is this a correct way to use infinitives? It would be nice if you gave me the full rule about it.

Both possible answers could be correct in different circumstances.

If the man speaking was describing a situation before he watched the movies, then "My first movie to watch was ..." would be correct.

If, however, he was describing the situation after he watched them, the correct sentence would be "The first movie I watched was ..."