The Official Canon 5D Mark III website says:
CF Cards (Type I); Compatible with UDMA CF cards; SD, SDHC, and SDXC Memory Cards
Note: No microSD is supported unless you use a microSD-to-SD adapter.
It's also worthwhile to mention, a MicroSD-to-SD adapter would not bring any loss of performance (either in writing or reading speeds) since the adapter is doing nothing but connecting the pins of the MicroSD card to the contacts of the SD slot.
The maximum size of CF or SD cards supported, 128 GB, is certainly supported for both CF and SD Cards.
I haven't yet found any information regarding 256 GB cards being supported by this camera.
Later edit: I have found a review of the camera specifying that Canon declares 256 GB cards will work just fine with the camera. Photo.net Review
The cards normally use the FAT32 file system but the 5D Mark III supports exFAT not only for SDXC but also for CF cards with storage capacities greater than 128GB. Maximum card size isn’t specified, but Canon commented that the latest 256GB cards work just fine and larger cards should work in the future. I can’t say for sure if the full 2TB limit of the file systems will be fully supported, but I think the day of 2TB cards is probably far enough away that it’s not really much of a concern (not to mention such cards would likely cost more than the camera…). UDMA mode 7 is supported.