720p and 1080p are marginally different when viewing media like TV, and 1080p is very high for playing games. Avoid plasma screens. There life is affected by how high you put the settings on the TV, you can also get images burned into the screen permantley (like channel number in top right and left screen) The best line of LCD Screens (in the UK atleast) Is samsungs current range,
the R76's.
Im not sure wether you have OLED (Organic Light Emmiting Diode, or Organic LED) released yet but thats supposed to be great, much sharper, brighter images than LCD and Plasma, supports full HD and above. A bit pricey though.
SED tv's are also good, i think there built on the principle of each pixel is like a Cathode Ray Tube out of your old CRT. Thus they are very bright and can be built indefinitely large.
720p is only 1280x720. Thats about perfect for playing games.