1. If you want the best TV for your money, join AVSForum and ask around
here. Generally it's better to read reviews and get expert opinions on a TV, rather than going to the store and picking the one you think looks best, because they almost never are.
2.If you xbox has an HDMI port, get this in preparation for your new TV. If it doesn't have one, then a component cable is a good second choice.
3. I'm not familiar with any headsets because I prefer surround sound, but yes, it does look like you'll need an additional adapter to use that if you intend to use an HDMI cable.
My links never seem to go through here, so here are the urls: