I've been using the 5D3 for a few months now with several different cards. I can confirm that firmware version 1.12 still has the slow write speed for the SD card slot. There is no support for UHS-1 (unlike the new T4i/650D) so there is no benefit to using the fastest SDHC/XC cards like the Sandisk Extreme Pro 95MB/s. There seems to be a ceiling of about 22MB/s so any card that is up to 3045MB/s is fine.
I'm not sure if the slot can be firmware upgraded to handle UHS-1 but it is definitely a silly thing Canon did and a negative for the camera.
As for card sizes, a 32GB will take over 1100 images or 44 minutes of ALL-I clips. The battery can last up to 2000+ shots so 64GB cards would be the best capacity to get for topside, non-stop shooting. Hope this info helps.
Edit: In the 5D3 manual, the minimum speed for SD cards for ALL-I video codec is 30MB/s. At 90+mbps, the speed of the ALL-I codec shouldn't be more than 15MB/s.