You need a few 100 more for smooth FPS on high settings in "most" games. Your budget is for a lower end system unless you buy used parts.
Intel i5-6500 and an nVidia 1060 should get you to good FPS but those two are almost at your budget on their own, without anything else. $200 USD for CPU and about $260-280 USD for the video card. For still good results, the Radeon RX 470 should also be OK and is probably better for a cheaper build.
If you can't spend any more than your listed budget, don't expect high settings at good FPS. You'd need a card like the RX 460 to fit in the budget, and this is not counting a monitor/keyboard/mouse/operating system. Windows for a new build is $100 just for that, another $160 or so for monitor/keyboard/mouse that are not junk.