The HDMI from laptop not displaying is just the laptop I think. Even if it doesn't, all it means is you have to use DVI-D + that headphone jack to connect to the monitor (unless you are using speakers) both of which should come with the PC parts.
The 'cleanness' is probably your laptop having a lower res than your monitor. In terms of picture HDMI = DVI-D except hdmi carries sound.
XI Wiki

can't wait to order this stuff and put it together.
