SONY. Think no further. You cannot go wrong with any 40 inches and above SONY for playing Games. This doesn't mean only Sony can fill your requirement, but all Sony has very less input lag which will help a lot during FPS and fast games. There are some TVs from other brands which has less input lag, but... but.... you need to do the homework.
Many Tvs which feasts us with beautiful movies and crisp videos will suck when it comes to gaming, even in game mode if you are heavily in to FPS games.