nothing will looked 'stretched.' In the game, you select the resolution you want to display, 1920x1200 or 1920x1080, depending what monitor you pick and the game will draw to that.
1920x1200 is a 16:10 ratio, while 1920x1080 is a 16:9 ratio screen (same as and hdtv).
If the monitor will be mostly used for games, id go with the 1920x1200 monitor. If he will be watching alot of movies or hd video on the monitor, the 1920x1080 may be better.