Most laptops feature a VGA out... so you can connect it to an external monitor as well. If you shop around ebay you might even be able to find a "Dock" for your laptop that will allow you to just plop it down onto to hook up to your monitor, mains, keyboard, mouse, etc. I have one for my IBM T20, it only cost me $8USD and I couldn't be happier with it.
As for a monitor. If your laptop supports DVI output you should look for an LCD with both DVI and VGA inputs, that way you can have them both connected at the same time and just use the monitor's built in switch.
Keep in mind that if you use a monitor you'll probably need speakers as well which will add cost.
Speakers + the 360 VGA cable could end up costing as much as it would to get a small LCD HDTV as opposed to a monitor, so keep that in mind.
If you DO go the PC monitor route I'd recommend picking up a widescreen monitor as the Xbox prefers outputting in widescreen format, a full screen monitor will show most games in letterbox or stretch them to fit (both of which are kind of ugly IMO). It's not necessary but it's preferred.
Regardless you'll need to pick up a monitor that has a "native resolution" that matches one of the following:
Fullscreen:
640 x 480
1024 x 768
1280 x 1024
Widescreen:
848 x 480
1280 x 720
1280 x 768
1360 x 768
if it doesn't use one of the above resolutions as it's "native" resolution then it will probably look like crap.