120hz and 240hz televisions post process in (they fake in) the extra frames which results in a bit of noticible lag in games and pc use in general. it is not noticible and actually looks a bit better for movies. the reason why it is post processed in is because they only take a 60hz signal.
some models do offer a game mode or 60hz mode but i have seen various reports of this not working propperly and people posting about the matter. there may be a workaround in some cases.
if you buy a 60hz panel then you do not have to worry about game mode and since you plan on using it almost exclusively for pc use it would be smart to at least give this thought. as for what you are missing out on for movies is 3d (which is gimmicky at best) and a smoother framerate (negligible in my opinion). since the framerate is locked at 60hz input on ANY model (60, 120 or 240hz) and hdmi output on video cards is 60hz you really have nothing to gain from buying a non 60hz screen.
60hz screens are also cheaper. i know for a fact that you can get a 46" sony bravia led backlit 1080p television for $750 on sale. you should be able to pick up a 40" for a little less. no smart tv, no special features, just barebones tv which is what should connect up best without issues.
of course the decision is completely up to you. dont believe me on the lag? search the forums here and you will see what i am talking about.