Fastest desktop screen capture method for capturing presently running application on desktop and casting it to an external monitor

I am creating a screen capture application which can capture presently running application on desktop (be it a fullscreen game or a video or simply desktop) and render it onto an external monitor.

I read various questions on stackoverflow and refered different blogs about screen capture using DirectX or GDI or OpenGL or Windows Media Encoder but I couldn't draw a definite conclusion as to which could be the fastest method for the purpose.

Any inputs are appreciated.

I am new to programming in general so I will learn the method which are expected to give me best results.