I think at 15' you are pretty far back so I think if it was my setup, I would be looking at size over picture quality at your budget. What about a 65" Panasonic S series. Some look down on this set here at avsfourm, but that far away... Perhaps one of the biggest Samsung Plasmas in one of the big, but with less feature models (not familiar with the Sammy model numbers). I think there is a 60" LG plasma that might be in your budget too, even that might work. Any plasma will show the fast motion of Nascar well (like down on the side wall when the all zoom past).
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