DVI is newer (digital) and slowly being found on newer graphics cards. VGA is older (analog), much older, but more commonly found. You can take advantage of DVI assuming your TV is able to take advantage of it. Simply put, DVI is only as good as your TV or monitor. If you're worried, go with VGA. Most current TVs should handle it just fine, but as always, your mileage may vary.
You'll want to look at Vista Home Premium edition. This contains the Media Center software. You will probably need a tuner card if you wish to watch TV and use your computer concurrently.