If it's just 2D, then perhaps it might be worth looking into SDL, which is already cross platform and seems pretty easy to learn. There are many tutorials on the net, but one particular site I remember is Lazy Foo's SDL Tutorials. You can also mix OpenGL with SDL, there are tutorials for that as well.
If you don't want to use SDL, and you are on windows, I would recommend DirectX. I do recognize that the choice between them ultimately ends up in a flame war pretty much anywhere on the Internet, but my understanding is that DirectX is geared towards game developers, so you will find many utility libraries, functions, and classes that might facilitate various tasks. With OpenGL, you would have the ability to write cross platform code, provided that the helper functionality such as image loading is also cross platform (For which there are indeed cross platform libraries).
So my bottom line is: Both are fine, OpenGL gives you cross platform code (Provided you write it), and DirectX gives you more game development oriented tools and libraries.
