LCDs have a lot of downsides that make them less than ideal for gaming. Particularly a used one you might pick up for $100. They might be superior for staring at in Microsoft word, but they are not the best gaming display.
Here is what would be happening with that 19" LCD monitor, game outputs CGA, your convertor scales that up to 640x480, which cause image degradation, your monitor then upscales that to its native resolution (probably 1600x1200) and you lose a LOT more image quality.