The 960 is still a decent card, your biggest issue is the CPU, it will cause FPS drops in many games at higher settings.
You will need to upgrade the CPU to get full benefits of a good video card.
For your budget, GTX 1060 6GB or RX 480 but you may want to think about keeping your card and upgrading the CPU first. You can use the 1150 socket Intel i5 if you want to keep your existing RAM.