If you are to max. out that $250 budget for the CPU, the best you can get is:PCPartPicker part list
/ Price breakdown by merchantCPU: AMD - Ryzen 5 1600X 3.6GHz 6-Core Processor
($245.98 @ PCM) Total:
$245.98Prices include shipping, taxes, and discounts when availableGenerated by PCPartPicker 2017-05-28 15:48 EDT-0400
orPCPartPicker part list
/ Price breakdown by merchantCPU: Intel - Core i5-7600K 3.8GHz Quad-Core Processor
($229.00 @ Amazon) Total:
$229.00Prices include shipping, taxes, and discounts when availableGenerated by PCPartPicker 2017-05-28 15:49 EDT-0400
The first option is 6-core/12-thread AMD CPU ideal for gaming AND multitasking. The second option is a 4-core/4-thread Intel CPU ideal for pure gaming. Both CPUs are overclockable (doesn't include a stock cooler so you need to purchase that separately). The AMD CPU needs an AM4-socket motherboard (ideally, a B350 or X370 mobo, which supports OC). The Intel CPU needs an LGA1151-socket motherboard (ideally, a Z270 mobo, which supports OC). Both CPUs will handle your GTX 960 2GB easily.
Getting any of those 2 GPUs will give you the opportunity to upgrade your GPU to a more powerful one in the future.