Personally, I'd learn OpenGL if I were you, especially considering you want to do 2D development.
I'm in the midst of trying to learn DirectX. There's a couple of issues I currently have with it:
1) Good luck finding an up to date tutorial. Most of the tutorials out there (like the ones on Gamedev) are from DX 8.0. The DX9.0c spec obsoleted a bunch of functions, from what I gathered, and you'll spend a lot of frusrating hours trying to get code to work.
2) Good luck finding a good DX9 book for that matter... I still haven't found one :P
3) If you download the SDK, there's some decent examples, but MS tends to go overboard in those and highlight thirty different ideas at once. As such, it's not for the faint of heart... I've also found that the tutorials I'd be really interested in aren't there (just the pre-compiled example).
Now, if you can put up with all that, DX does have some really cool things going for it, like keyboard/mouse interface already built in, music and sound support, and networking support.... As I understand it, you'd have to implement all of that yourself in OpenGL (though I'm told there's a couple of libraries out there that will help...)
Hope that helps