**WARNING:
Monitors tend to have VGA or DVI inputs, and a few new ones have HDMI but all should provide for different resolutions to be set from 640x480 on up.
HDTV's have HDMI as the primary input and may have a VGA PC input. While the VGA PC input allows for different resolutions so your HDTV acts just like a monitor, the HDMI does not. For HDMI you'll have to choose 480i, 480p, 720p, 1080i or 1080p.
If you are going to input 720p you'll have to choose 1280x720 as your resolution. You can NOT CHANGE this in a game. This is the ONLY resolution you have and you may also have to tweak your video card setup to prevent overscanning. The only real advantage to using HDMI if you have a VGA PC input is BluRay compatibility. You can bypass this by ripping the movie to your hard drive thus removing HDCP, using special software to ignore HDCP or using BOTH inputs and toggling between them with your TV remote.
If anybody reads this and hasn't yet purchased an HDTV I recommend getting one, or waiting for one if not available that has an HDMI PC input so you have full video, audio, HDCP and your choice of computer resolutions. *Note the ATI HD3870 has HDMI output but the audio is not a full audio chip and only works with movies. I couldn't wait but hopefully we'll see a solution that allows for true HDMI output. The best solution will be a motherboard that can TURN OFF the high end graphics card when not gaming and use the onboard solution. Therefore, we'll be looking for true HDMI out from the motherboard.
Question:
My picture is fuzzy.
Answer:
If you are using an HDTV that is 1366x768 (768 lines) and have used the HDMI input and sent a 1280x720 signal (720p) the HDTV will scale to fit the screen so smaller text looks incorrect. If you have a PC input (likely VGA) use it.
Question:
How much should I spend on a digital cable?
Answer:
Not much. Barring incredibly low quality or other incompatibilities even the cheapest cables work perfect. If you see a picture with no speckles than the cable is working perfectly. Don't be ripped of by getting a $150 HDMI cable when a $15 cable would look EXACTLY THE SAME.