If just 24" and you have not already bought/own it, better to be a monitor, as it will have the much lower response time (vs most tv's) required to reduce "ghosting" in fast paced games such as FPS and fast racer's.
Especially If you're after 1080p gaming, prepare yourself to drop the gaming video quality settings, using such a low end, outdated for gaming GPU. This deserves an upgrade priority over any other purchases after the motherboard, such as aforementioned "TV."
What is the rest of your spec?