DirectX is probably your best bet if it's going to be run on Windows based machines. DirectX is a collection of API's:
DirectX Graphics - Previously DirectDraw[2D] & Direct3D[3D]
DirectAudio - Combines DirectSound & DirectMusic
DirectInput - Input Devices, Joysticks etc
DirectPlay - Multiplayer gamming over LAN,WAN,Modem etc
DirectShow - Multimedia ie mpeg, video etc
It's nice to have a range of API's that not only maximise your hardware potential but use the same structure which makes programming much easier.
I actually prefer OpenGL as a graphics only API, but it still leaves the problem of what to do about sound etc. It is of course multiplatform so if your programming in C/C++ for Windows & Linux/Unix etc life is easier. You still however have to hope that your graphics card fully supports OpenGL (Many manufacturers are make more of an effort on this front).
Your other alternatives are to use the basic Windows API calls, which is fine in some cases but kiss goodbye to your acceleration.
Or of course ignore Windows altogether and look at the newer VESA standards for cards (although yet again not worth it, lack of support & acceleration).
The coder formerly known as Twynklet.