there's no way anyone's gonna tip over a cabinet (even with a flatscreen) by button mashing alone, but if you're talking a 12" deep cab, your control panel had better be the "inside" style that classic cabs have rather than an overhanging one, because that might topple a skinny machine. BUT putting a flatscreen inside a normal-sized cabinet wouldn't hurt, because those can already balance and take weight on the control panel without the monitor.
Most people use either TVs, arcade monitors or big VGA ones. LCD screens do not support lightguns, and aren't as authentic looking as TVs and arcade monitors or as wide-angle-viewable as the other three. (If you have a wraparound control panel, the view angle of the side players could get quite large indeed.)