Normally, you wont be using GDI and DirectX at the same time. You may use some GDI functions to read in image file formats that DirectX doesnt support, but as far as actual drawing to the screen youll most likely use one or the other.
What kind of program did you have in mind? Do you just want cool effects, or were you writing a game?
DirectDraw doesnt support alpha blending (translucency) but does support color keys (transparent regions). Direct3D support pretty much everything, but the learning curve is steeper.
If you want DirectX and normal window controls to intermix (such as a textbox), you might have problems. With GDI+ you probably wont have any issues.
-Nerseus