Re: Connecting my monitor to the CPU
VGA is an analog signal and is more susceptible to interference, while DVI is digital, and is not. Usually, you will not notice much of a difference in image quality between the two. Although in some cases I have noticed a marginal difference. If DVI is available, I use that. If only VGA is available, I don't worry about it.
I have heard that DVI might have some advantages such as higher refresh rates and such that would benefit gamers. But I don't have a source on that.
EDIT: sorry I was thinking of DVI, not HDMI. But essentially they are comparable as they are both digital signals that support high resolutions. But as celery said, HDMI can support audio. For a computer I would stick with DVI and for TV, use HDMI.