What should I replace on iPhone 3GS shattered screen?

I dropped my iPhone from about 6 feet. The glass screen shattered pretty badly. It had previously fallen and it had a nick on mid- screen and almost at the right edge of it, that's where crack initiated shattered. I see different parts that can be replaced, if the LCD is working fine, no dots or anything spilled, the sensitivity on the touch screen is also fine. Should I just get the glass replacement or the complete display assembly. What do you recommend?

Thanks