You fail to miss the point in the 'burning' issue. The reason why plasma televisions are not suited for gaming is that some games tend to have something which stays in the screen ALWAYS. The effect it has on the TV varies from model to model, but to be sure I'd suggest that if you plan on playing for over an hour, you take little breaks from time to time and flush some varying picture through the TV for a minute or two.
The thing that makes plasma TVs 'better' than LCD is the contrast. Since LCD technology means that the picture is made by series of light sources, it is impossible to make a real black picture. When the screen is very dark, as it often is in games and movies, the lightning-based effect can be clearly seen in LCD TVs.
As for the resolution, almost all TVs nowadays have 1366x768. If you REALLY must have better, it'd have to be 1920x1080 which is the highest High defignition resolution soon-to-be-available. Apparently Play Station 3 will output 1080p picture whereas xbox 360 outputs 'only' 720p. But as far as I know, the very few TV models that actually support the 1080p resolution nowadays are still rediculously expensive. And you probably won't be 'needing' the 1080p instead of 720p in another ~5 years.
My advice to you is: get a 1366x768 LCD of the same size. Just make sure it has HDMI and component inputs.