The HD number refers to vertical resolution - The second number in the screen resolutions we use would be the corresponding. 1920 is the horizontal rez, tho. So you'd need a widescreen computer screen that does 1920 x 1080. You start finding those at around 22" widescreen - $300~ish for a good one.
Actually, 22" monitors are incapable of displaying 1080p as they generally have a native resolution of 1680x1050. 24" monitors and up are the only ones with resolutions of 1920x1200 and they're usually around $700, although some can be found for a little over $600.