For an Xbox, I would personally go with a good quality 1080p HDTV that uses an IPS panel and is known to have low input lag and good motion handling.
As for what size, it really depends on how far you plan to sit from the screen.
The benefit of a monitor is that it is designed for use with a PC- so input lag is relatively tiny, the pixel density is high, they are relatively small in size (as they are designed to be used close to the user who is sitting at a desk) and don't tend to have good scalers (so not ideal for running non-native resolution content). These features are very good for PC gamers (and generally all PC users) but not ideal for use with a console (unless you plan to sit very close to it).