HDMI LCD Monitor

Hey,
I am new to this forum and in need of some help. I had an old Hp f1503 flat panel monitor lying around collecting dust, so I decided to use it as an T.V monitor. I purchased a T.V tuner that outputs VGA and has inputs such as coaxle, audio/video, etc... I can get everything to work, but I was wondering if there was a way to have better picture quality, such as H.D. I am trying to be able to play XBox360 with a better picture quality. I found a way to buy a Vga to Dvi converter and then purchase the necassary HD cables. My question is, will this work with my T.V tuner, will I have a better video quality while playing XbOx360, and will it be worth the time and money to do it?
Thanks for the help!