There is gaming involved too though right? A 8800 gtx will not help with video editing unless you're going 3d rendering for the videos.
But at any rate you're asking about the monitor. "HD" is basically just a set of resolutions (and frame rates, but whatever) that includes 1280x720 (720p), 1920x1080 (1080p) and such.
Traditionally monitors have been way ahead of TVs in resolution so it's not really a big deal to look for an "HD" monitor. HD resolutions are widescreen, do you know if you dad wants to have a widescreen (16:9 / 16:10) monitor or a 4:3 one or a 5:4 one?
Is this professional video editing and viewing or just casual stuff?