Whats included in that budget? Just the cpu and motherboard? Any specific reason why it has to be AMD, for gaming Intel currenlty has the edge. And depending on what that budget includes that maybe the best bang for your buck.
GPU will take care of your gaming and rendering needs, for that GTX 970 will have enough juice to fire upto 1440p single monitor set-up at 120/144 Hz at max setting excluding games like Witcher 3/ star citizen etc which at times put 980's and 390x to shame.