Configuring Xbox 360?

Okay so I bought a 360 recently. And I know a lot of people have been saying that you need to tweak it by yourself, so for the record I'll give you my TV specs:

LG 37LG60 37-Inch 1080p LCD HDTV, It's a great TV with some really nice native 1080p quality.

So my xbox has been working perfectly, except for a few other details. First off, the refresh rate. My TV has a 120hz refresh rate, while I can't change the xbox's refresh rate any more than 50hz. Secondly, my TV has native 1080p, but most games are native 720p, what should I use? Aside from that, If you can check out my TV I'd really like some in depth details on what I should set up my TV and my xbox 360 to.

Only thing I can recommend doing, if you haven't already, is turning down the sharpness on the TV. Other than that you can adjust the brightness etc. to your liking, but I'd leave it personally if it looks good to you.

Doesn't turning down the sharpness make the screen a lot blurrier?

@matthewsto: I have a Samsung TV, and the scale for the Sharpness goes all the way up to 100, I actually have it on 4 and it looks perfect. Every TV is different but for gaming, it is recommended to turn down the Sharpness for a better picture. Find a balance that works with you, turn it down but maybe not all the way down.