You should NOT use VGA. VGA is analog. On your video card all the data is processed in digital then at the output instead of going to DVI/HDMI it first goest to a D/A (Digital to Analog) chip. It reaches the TV via the VGA cable then is converted BACK to digital via an A/D chip.
HDMI vs DVI:
HDMI is DVI + AUDIO. The video portion is NO different.
The only reason to get the HDMI cable is to use the built-in speakers. In my opinion NONE of the speakers in a flat monitor are very good.
I would definitely be inclined to buy a second set of speakers. As for the DVI or HDMI cable you can still use the HDMI cable and turn the speakers off, but I assume you have a DVI cable already.
I'd use the DVI cable and buy a nice set of speakers. They vary in quality but even a $40 set of 2.0 speakers is likely to be superior. Audio quality also depends on the sound card or onboard sound chip. An example of really good sound quality is:
Auzentech X-Fi Forte + M-Audio AV40
I've purchased an excellent HDMI v1.3b online for $11 (plus shipping). There is NO difference in the signal as it is digital. Don't be fooled by $180 HDMI cables.
This is a Canadian site, but use the price as a reference and shop around: http://www.cablesalescanada.com/
The problem with HDMI is that, unless you have one laying around for the price of the cable and shipping it's likely you can walk down to a local store and get a cheap set of speakers with superior sound to the ones in your monitor.