There's not much difference between a regular LCD and a LED variant LCD as far as getting more out of your games is concerned, the LED is just a little slimmer and a little more power efficient. Honestly I wouldn't worry about getting a LED display unless you're going 40" or up. At 24" and less a LED would hardly save you more power then a regular LCD would, but would still cost more cash when getting it at the store.
As for a monitor versus TV, there really isn't much difference unless their specs are different. There was a time when there was a gigantic difference between a 1024x768 vga monitor and a 480i tv over composite. These days though, the 1920x1080 at 60hz the monitor does is less and less different then the 1920x1080 at 60hz the tv does, assuming it's the same size. Granted, at 24" most of the TV's you'd be seeing are only going to have 720p native. Just what kinds of "games" are you talking about playing? If it's for your console that won't matter as most of those games are only rendered natively at 720p anyway. If it's for PC games, I'd say get a monitor off Newegg as it's far more common place to play PC titles in native 1080p.