As pointed out by several of other people, If you are planning to port your "Game" to other platforms other than windows, you better start using OpenGL.
If it is just a simple 2D game, and you won't need a 3D support for now, SDL would be a better choice, later you can combine "SDL" and "OpenGL" together. ( you can directly use openGL from SDL, it even has it's own header in SDL ).
At the same time, DirectX offers features that neither OpenGL, nor SDL can give you. OpenGL is way behind DirectX. [ OpenGL 3.0 is nothing more than an incremental update, the API hasn't changed much since 2.x ].
So if you are planning to write a game for windows, just use "DirectX", if not "OpenGL" and "Sdl".
Finally if you aren't looking for headaches just use a GameEngine, e.g. C4 Engine. Believe me when you go for 3D you have no choice, since there are so many topics that will need a lot of time to "Dig" and "Learn".