Hitachi is a good brand. RCA not so much.
For gaming, have a look at DLP technology. There is NO BURN IN issues for vidgames. The picture quality is excellent and comes in big screen sizes. The Hitachi you listed was $1700, so at BB I found a 42" for $2000
http://www.bestbuy.com/site/olspage.jsp ... 5366829183
Consider a DLP projector:
http://www.bestbuy.com/site/olspage.jsp ... 0266874767 You would have to budget for a screen.
Both are close to your price range. Save up a little bit more if it is necessary. Prices are falling all the time. Waiting a few months/Boxing day sales, you can get more screen real estate for the same money.