Sony KDL22l4000, Sharp LC22SB24U and LG 22LG30 are my first choice with your price range, Sony is more expensive next is Shard and least is LG. But because you're going to use the TV for PS3; I suggest you to buy a PC Monitor instead, with 2 ms GTG as you might encounter ghosting with the TVs I suggest above.
For that Benq E2400HD, LG W2442PA-BF , Samsung T240HD, HP w2558hc, Gateway FHD2401 or Dell UltraSharp 2208WFP monitors are good for PS3.