Yes, as Sut explained, what you use depends on the connections available on your equipment. The wire itself is exactly the same for DVI and HDMI; the difference is whether both ends have a DVI or HDMI connector, or there's one of each.
A little more on your "quality" concern. HDMI is unfortunately creating yet another opportunity to sell pieces of wire at rip-off prices.
Here's a review from the source Randy linked and
here's another price comment. The link there to Better Cables has good info, although they don't happen to mention that equal cabling is available for about a tenth of what they charge for their "Display Magic".
