To get 3D, you'll need a 3D-ready TV and active 3D glasses. Even though your television says it's 240Hz refresh rate (I think I have that same one), that's only it's output speed. The input speed is 60Hz. The output speed is after image enhancements and processing to reduce / eliminate blurring.
It will be cool to game on the larger 40-inch screen, though 1080p on 40-inches is the same resolution as 1080p on a 23".