The "ultra thick" premium one may not even work if it's anything like the Wii U, which had issues with thick screen protectors rendering the system unplayable, so non-premium might actually be better.
If it's regarding touch capabilities, I think it wouldn't be as much an issue this time.
DS, 3DS, and Wii U all used resistive touch screens, but for the first time Nintendo has switched (not a pun) to a capacitive touch screen like smart phones use.