I hope my response is not too late...
A month ago I decided to do this too. My screen wires are already finished and now I'm busy with a Wiikey Fusion on my Gamecube.
Now, my question is: what do you want to change in the gamecube?
About the screen: its quite easy but it depends on the way you choose: do you want composite video or RGB or even component?
If you do not have the psone screen its a bit more difficult because you have to find out the video and audio inputs yourself.