If you don't have a 360 w/ HDMI output, you'd need a component -> DVI converter, and those aren't cheap. Probably $150 & up although I haven't priced them lately. I don't know if it would work with the 30" because no converter I know of supports dual-link DVI and I don't know if that model ACD can sync at lower resolutions.
Yeah, for that price, you might be better off buying a Dell monitor that supports A/V inputs. But if you're going to do drop 200 either way, I recommend saving up and buying a small Samsung TV for 200 more; you can still set it up on your desk but you'll get your component quality signal and better sound. Size shouldn't be too much of an issue when you're 14 inches away from the screen.
would it be an HD image?