PLaying the xbox 360 on LCD monitor or HDTV

I am in the market for a new display fir my xbox 360. I was looking to get a LCD tv as I am now playing my 360 through an old flat panel monitor. I was just wondering on a computer monitor can I get 1080 out of a 24 inch monitor and if so is it worth it or should i go with the tv. The only problem with the TV is that it would just be more wasted space in my small apartment, and the obvious price difference, also the fact that i would only really use it for gaming only. If the mionitor is the way to go any suggestions. I was looking at a HP 23 inch with 3000:1 ratio or an acer which both of these models have the 1920x1080 resolution.