Use of different cable types, may greatly affect your viewing quality depending on your output device (DVD, PC GFX card, console,TV box & etc), as well as your viewing device (PC Monitor or HDTV) Some combinations work great - others work dreadfully.
DVI can only send video signals
The difference between dual and single link DVI is an increased bandwidth. Not all GFX and other products support dual link DVI. Since your screens native resolution is below a single link DVI`s maximum resolution with a good margine, you will have no benifits with it at all.
A single link DVI can do a teoretical resolution of 1920x1200 by using reduced blanking mode (blanking mode is something CRT needs, not LCD's). But, a single link DVI is optimal at 1600x1200 and anything above is dependent much on cable and also on hardware connected.
HDMI cables sends both video and audio signals.