here is the deal with t.v.'s
240 is really a 120 hertz with overscan blur reduction.
120 is really a 60 hertz with overscan blur reduction.
get a 240 hertz t.v. and use it in game mode. never use any of the other modes.
game mode reduces input lag.
Also unless the t.v. supports hdmi 2.0b(
http://www.hdmi.org/manufacturer/hdmi_2_0/) or display port, it will never be a as good for gaming as a comparable monitor.
Also check your graphics card to make sure it supports the newer hdmi and displayport modes.
unless you are talking about console gaming... and then none of this matters because you are really stuck at 30-60fps regardless of the t.v.