Windows 8 and Windows 8.1 have been supporting DirectX API 11.0 and 11.1 practically since they were birthed. Officially as said above it is recommended to use an AMD series 7000 and above or the nVidia series 600 and above. Frankly any graphics card will do though as Windows 8 is backward compatible with DirectX.
I recommend, if you're going for a nice cheaper option, nVidia GTX660. The performance is reasonably good and AMD is moving slowly away from DirectX and toward Mantle. I cannot provide any help for you concerning Mantle and how that works with Windows as I use nVidia.
Regards,