Both DVI and HDMI will deliver a 1920x1080p signal to that TV for both BD movies, gaming, and general computer use, the choice really is whether you want to run a seperate audio cable or not. As spinny mentioned, HMDI can transmit both audio and video.
There is no picture quality difference between DVI and HMDI. However, DVI has a max cable length of 10 meters while HMDI has no defined max cable length.
Lastly, do not get ripped off into buying a more expensive cable under the guise that it is "better" than a cheaper one. The $25 generic brand 3ft cable from Radio Shack is just as good as the 3ft $100 Monster Cable from Best Buy.