What tv has the best picture quality under $600?

LG 42LV4400

With LED picture quality and a TruMotion 120Hz refresh rate, sports and fast action movies on the LV4400 never looked better. read more...

I bought this bad boy in August and I like it a lot. I was able to get it on sale for 499.99, so I eas pretty pleased (Canadian price)

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LG 42LV3500

There's nothing like watching your favorite entertainment on the 42LV3500 in crystal clear Full HD, with the dazzling colors of an LED display. Movies are immersive. Sports are more exciting. Your favorite shows look better than ever. It's time to... read more...

This might be your best option in terms of picture quality. It's gonna come in slightly over your price point, but not too much, and I think it's worth the price. Is 42" a good size for your room? Seems good to me... no too big or too small.
So it's full HD, 1080p. The only downside here is refresh rate.... only 60Hz. This will only be an issue if you like watching sports a lot or fast paced video games. Anything moving too quickly might blur a little bit, but nothing too bad. The main thing is pic quality, and it will be great.
It also has Picture Wizard II, which helps make for some easy picture calibration.