For the frame rate, the speed of the flash cards only comes into play if you end up exceeding the size of the memory buffer. So let's say you're shooting full size RAW, and the memory buffer can hold up to 12 images. You can hold up to 12 images before the camera needs to stop taking photos until a photo is flushed to the memory cards. In reality it tends to exceed the memory buffer size some because it writes out to the flash cards while you are still taking photos. So with the fastest cards (which in the 5d3 is the CF UDMA7 cards) you can pretty easily get several extra frames before the camera increases the time between photos.
So, if you are shooting 1-2 frames per second on average, you likely will be fine so long as you get an SD card that will max out the speed that the 5d3 can write to it. Now, for downloads, you may want the faster UHS-1 SD cards, but that's purely a matter of workflow and amount of time it will take.
You speak of "better quality files", but what does that mean? The RAW files on the 5d3 is of course somewhat different than the 5d2. They are different cameras. But both will include proper checksums, preview jpg, meta-data, etc. The Digic5 generally just gives a faster CPU, as well as more memory and possibly more readout line capabilities, but that requires the sensor to be able to handle those as well.