I have a 32" HDTV with hdmi but I dont use it, at adds in a noticeable amount of lag even when set to game in the menu. My 25" running on component has nearly no additional lag because of the less amount of processing needed. I can read the signs and the words on things, just not a longer distance as some people. So I play a short defense game style to match the tv.
Used a Visio 42 inch, 1080p, 240hz, 8ms, LCD TV for about a year and my gaming went from challenging to impossible. Bbullets wouldn't even make contact anymore because the input lag gets worse with time. Just buoght a Samsung 27inch, 1080p, 60hz, 2ms, LED monitor with 2 HDMI inputs, and gaming is AWESOME now. No bluring with turning, sharp image details I couldn't see on the TV. It's my TV most of the time now too. I will never use a TV for games again.
Anything 5 ms or lower response time is fine, and will not be noticeable. Monitors with low response time and "Game Mode" are amongst the best to play on regarding everything being displayed on screen in time, and without a ghosting effect.
Anything from 22-24 inches is ideal for gaming, and is the range used for Competitive gaming monitors. Keep in mind that the bigger the screen, the more area for your eyes to cover, and the more pixels the TV will have to refresh every second, causing more of a delay.
BenQ, Asus, and Acer, are top-tier gaming monitor brands.
Don't just look at the response time, look into the input lag as well. There are monitors with 5ms response time but still have 2 frames of input lag or more. What you should look for is sub 1-frame of input lag and very low response time.
For console gaming, the best one is currently the BenQ RL2455HM. It is specifically built for console gaming. It has sub 1-frame of input lag and a response time of 1 millisecond. It will eliminate input lag and any lag you encounter in game will be caused by the internet.
Trust me, this thing will help you a lot and improve your game. Get this monitor, a Scuf controller, and Kontrol Freeks and you'll be dominating.