Your cheapest and still reasonablely high quality 1080p compatible computer monitor would be the 24" Soyo that Office Max advertises every few weeks for $300.
Get a Samsung. for computer monitors u have to go over 24 inches to get 1080p. i have a 20" Sammy max resolution 1680 X 1050, not quite 1080p. hooked up my 360 to it and there was no option to run it at 1080p, but it still looks great.