This is a pretty nonsensical question, simply because there is not a one fits all scenario. Look at old VGA DOS games. Those have a palette of 256 colours at once. Some of them do clever stuff to change colours between levels and other things.
Dor example, look at Doom, Heretic, or Quake. Those games all only have 256 colours on screen max at any given time, but they have very different atmospheres. And that has a lot to do with which colours were picked by the artists. In general when it comes to making games for art you should always develop your palette with your intended assets and the game as a whole in mind. What feelings to you want to evoke, what things are important to stand out, how do you guide the player (can be done with colours and lights for example, etc.