my advice would be to use the money on a better card than on a 960 and a new monitor(or wait for the new 1080/1070). any card can produce more than 60 hz if the load is simple enough. turning down graphical settings or output resolution will increase your fps, and if you surpass the refresh rate of your monitor, the monitor will simply ignore the extra frames. vsync forces the gpu to limit itself to 60hz(or other settings you choose sometimes) to match the monitor's refresh rate.
however, i would personally prefer running a game prettier than uglier at a higher refresh rate, and a 960 will not be getting you high or ultra settings at 60hz let alone better on modern next gen games. they're very demanding of the gpu.
just my...