Seems to be a popular topic lately...

The problem is going to be the TV tuner, which will almost certainly use about a 2 second buffer/delay in order to ensure smooth playback. For watching TV, a 2 second delay is meaningless, but for a game console it's generally unacceptable.

If you don't have a monitor that has native composite/component/s-video inputs, then you should just abandon the whole idea right now, and hook the Wii to your TV. There's no other good way to do this with computer equipment.