Hello, if i was you i would go for a gtx 1060 6gb, i know it will go over your budget, but 3gb of vram is just not almost not enough in games anymore. If you're planning to be upgrading the gpu fast than it's fine, but because of the 3gb vram it won't be enough for a long time. And 6gb of vram will be enough for a long time. So if you're planning to play the newest games, and you want to keep your gpu for a while, go for a gtx 1060 6gb. However, if you're not planning to keep your gpu for very long, than you can go for the gtx 1060 3gb. The gtx 1060 6gb is just more future-proof because of the 6gb vram instead of 3gb vram.
Get a better PSU like a Corsair CXM or CX (2017)
You need to use DDR4 RAM
Swap the case for something like a Cougar MX330 and toss in a 120GB or 240GB SSD