Where to begin.
All computer monitors are progressive scan. Computer monitors are rarely 16:9, even the wide screen monitors; 16:10 is the default widescreen monitor ratio.
360 outputs VGA - most high end LCDs offer both DVI and VGA, so that is an option.
If you have a DVI port, and a console that supports HDMI, there are cables that do HDMI to DVI. A quick googling brings them up for cheap.
As for component - its just really not worth it. The conversion boxes suck, unless you pick up a cable that has adapted component to VGA.
"Suck on it" -vgchartz mod