Which career should you study to be a video game designer, there are many different areas to be a game designer. Here's what I think are the keys areas to every game: 2D/3D Designer, Game Tester, Game Programmer, and Video Game Writer.
2D/3D Designer are the ones who create the models of the character in 2D or 3D.
Game Testers are the ones who tests game and give feedback and may learn how these functions work in the game which could lead you to upper jobs in each company.
Game Programmers are the ones who write the codes and functions of the game, levels, and characters.
Video Game Writers are the ones who writes the plots, dialogues, the character creations, and developments of the video game.
Depending where you live and what you want to learn, you can go from there. I would just dive into one of the game engine programs to get the feel.
Unity 3D is the highest quality game creation engine I have used. And, you can learn how to use the program in definite by learning through the tutorials on Unity.