DirectX or OpenGL? What's for me?

I've been programming for a year; and I have a all text color RPG engine to show for it. I have knowlege of the C fundamentals and a little bit about C++ OOP.

I've done just a little windows programing; the basics of creating a window and whatnot.

I have a mathmatical education up to Algebra II, and I'll be taking Geometry and Trig next year.

I want to eventually code 3D games; should I learn 2D first?

Coding multi-platform is nice; but isn't totally neccesary.

What should I learn? Here's my opinion of what I think I should do.

Learn the Windows GDI
Learn DirectX for 2D
Learn OpenGL for 3D.

How do you think that sounds? Is it neccesary to do 2D before 3D? What do you think I should do?

I think you should start with windows GDI, especially the bitmap blitting functions (blitting a memory bitmap to a window).

Then I would start with OpenGL, although it has less functionality than DirectX it is easier to understand, and has less overhead. Added to that it is cross-platform.

after that you can start with DirectX.

I only know OpenGL and I heard DirectX is a bit more complicated for the beginner.
On the other hand, OpenGL becomes a bit unstructured once you want to do more than the basic stuff (i.e.shaders).

There are tons of posts about this topic in the gaming board. You should have a look there. Confuted will probably suggest DirectX while Silvercord will try to convince you to use OpenGL ;)
However, in case you'll ever want to try another OS or use graphics for more than just games (prof. 3D-software), OpenGL is definetly the way to go ;)

DirectX is not for the faint of heart and I recommend getting a book on it before attempting to code using it. DirectX is the pinnacle of structure, sometimes to its own and your chagrin.

OpenGL is easier but it is rather unstructured as opposed to COM and DirectX - as was stated earlier.

I wouldn't even bother with Windows GDI - it's useless, slow, clunky, and way to confuscated to use in any large graphics oriented project.

OpenGL isn't unstructured, and it isn't worse than DirectX. The thing is that they two take different a different approach. DirectX uses a COM approach, OpenGL uses an state machine approach. I rather use state machine than COM.