In terms of quality it goes (from highest to lowest): HDMI, component, scart
HDMI can transmit 1080p, with component transmitting 720p, and scart transmitting 576i. If you've already got a 360, you'll need to check if it's one of the newer (in the last year or so) models. Originally the 360's didn't have a HDMI connection, so it's worth looking round the back of the box to see.
If you do have an 'older' 360, you also have the option of getting a 360-specific VGA cable. This can also transmit 1080p, although it's probably not as clear as the HDMI. I've been using the component cable for a couple of years now, and am very happy with the results. All games look extremely sharp and clear on my HDTV.