For that budget the best are the Radeon Rx 580 8GB and GeForce GTX 1070 8GB. The GTX 1070 8GB is faster by far. However, you are limited to a single fan card for your budget.
http://www.guru3d.com/articles_pages/msi_radeon_rx_580_gaming_x_review,1.html
If your case is big and roomy look at dual and triple fan models. They normally run the coolest and quietest. Normally they overclock the best.
If you have a small case which can handle a full-length card. Such as mini-ITX or cube style gamer cases. Get a blower style card. The reason being you don't have room to recirculate air. So, you need a high static pressure blower which will take cool air from the case and push the hot exhaust air out the rear. They aren't as cool and are louder than multi-fan cards. So, you should only look at them when circumstances dictate.
Single fan cards also run louder and hotter. I'd only consider them if your case doesn't allow full length cards or if they have a considerably price advantage.
Any of these should do. As far as GTX 580 8GB are concerned.
https://uk.pcpartpicker.com/products/video-card/#X=19445,35741&r=32768,24576,16384,12288,11264,8192,6144&sort=a8&c=391
The absolute fastest you can buy is the GeForce GTX 1070 8GB. Which has a big performance advantage. Personally, I would likely end up buying the 1070. Since it is such a substantial improvement. You just have to live with some extra noise.
https://uk.pcpartpicker.com/product/8fgPxr/msi-geforce-gtx-1070-8gb-video-card-gtx-1070-aero-itx-8g-oc