hdtv is anything 480p (pixels on the tv screen) and up, wether it be LCD, DLP, Tube, etc. (types if display methods).
LCD is fine and will look awesome, especially for gaming.
Unless you really care about this kid there is no need for the HDMI or DVI input, although more current/high end tvs have it automatically. The xbox360 only has a component output anyways, so HDMI isn't an option for gaming. The only time he would need HDMI is with a dvd player or set top box from cable/satelite, and even then it's still optional.