Unfortunately, I think your budget is a little small to want to build an effective computer with a focus in both like that. An i7 for rendering purposes is going to use roughly half your budget and a nice video card for gaming will likely use 1/3=1/2 your budget as well. So I guess the best way to balance that would be to suffer for an i5 (Skylake 6600K $240) which will still render okay and game well for $100 less than an i7 (typically), and a GPU such as a 960 which goes for around $220 and uses around 150W. At least 8GB of RAM, more if you have a higher focus in rendering.