I'd recommend SDL (http://www.libsdl.org/) for 2D, it was where I first started with graphics stuff and it was pretty easy to use, even though I barely knew C++ at the time.
ThisThis (mirror) is the set of tutorials that I started with and found very useful (they were a bit dated even ~4 years ago when I worked through them, but I don't think SDL has changed much and they should still be relevant).
SDL also does input handling and SDL_Mixer can do basic audio.
I've never worked with DirectDraw or OpenGL for 2D stuff, so I can't comment there, but I can definitely recommend SDL.