Just to clear things up a bit.
Current xbox is 1024x720p (if you have an NTSC box, or chipped box). Though most games are usually 480p (NTSC) and 576i (PAL).
Xbox360 will output 1280x720p (16:9) via component and 1024x768 (4:3) via VGA output. If you want widescreen HD you therefore need a component ready TV, not a VGA monitor. Either way, it will look nice.
If you're buying a TV for the 360, watch the resolution, most plasmas kick out a resolution of 1024x720p not 1280x720p, so there will be some downscaling. I went LCD for pixel per pixel resolution.
The 360 will have no DVI or HDMI output.
The full on 360 pack (as opposed to the core pack) will come with HD component leads in the box, which is nice. The VGA lead is an optional accessory.