The "hi-res pack" doesn't mean screen size, it means texture size. The plane is "so big" and the texture stretches to fit. 1024 textures have the most pixels and show the most detail. 512 are a slight step down (but still decent). Anything below 1024 resamples upwards to fit the plane, this is why you get blurry textures.
The downside is they take a lot more resources the higher you go on the texture size. I think your system can handle it, though.
And, to get the best pixel quality regardless of texture settings or other options, you'll want to run AH at your monitor's native (max) resolution. I checked the link you gave, this would be 1680 x 1050.