Das wäre meine Idee:

MSI B350 TOMAHAWK (AM4, AMD B350, ATX)
Corsair CX600 (600W)
Samsung 850 EVO Basic (500GB, 2.5")
Damit sparst du 193.50
damit liegt gerade diese gtx 1070 drin:
Gigabyte GeForce GTX 1070 G1 Gaming (8GB, High End)

I agree with the "previous speaker" (Amey1990).
Except for the power supply: most of the cheap Corsair PSUs are not really good (CS & VS & yellow RM series).
The prices of the GPUs are unfortunately still overpriced (but slowly going down at the moment). And for 595.- you can get a much better Gigabyte GeForce GTX 1080, instead of a 1070 for 540... A gtx1060 6GB is not worth 350.- for me.
Maybe an rx vega 56 would be interesting for you. which is supposed to be between an rx580/1060 and a gtx1070 in terms of price and performance.

The components would fit, but I think you can get much more out of your budget. Take a B350 motherboard that's about 100 cheaper, a 2.5'' SSD that's about 80 cheaper, and a PSU that's about 40 cheaper. Take the money and put it into a better graphics card and possibly a better processor.

Thanks for the suggestions but one more question:
Is 16 GB RAM necessary or would 8 be enough?