I do something similar for my cable box on my monitor. I use a HDMI to DVI. HD channels aren't exactly 1080 or 720 perhaps but it works nice.
Go with the DVI to HDMI wire but make sure you're getting the right female / male connectors (i.e. make sure they can be either plugged into or plugged depending)
Edit: Make sure that if you go with the DVI to HDMI option that you get the audio wire too because DVI does not support audio.