The 360 has multiple output options. I bought the VGA cable for it and it works just fine, in fact, it has much, much quicker response time than any HDTV I've ever used (ie, no HD lag). You simply hook up the cable, turn on the 360, and go into system settings, then graphics, then output resolution, where it has a huge amount of possible output resolutions. My monitor is an odd 5:4 monitor, 1280x1024, and the 360 is indeed capable of outputting in that resolution and I was pleasantly surprised at how well Halo 3 (my main game) runs and looks on it.
I fully recommend getting a docking cradle and running a dual-screen setup for whatever you buy.
Also, don't buy a Gateway. They are utterly terrible laptops that can't hold up to anything. You have no idea how many Gateway returns I saw while working at Office Depot where the screens, backlights, hard drives, just died, and in one case, the screen simply snapped off when he picked it up by the hinge.