Any SDHC card will work on a 3DS, so thats up to 32 gigs.
If you for some reason buy an SDXC with 128gb, i don't think that would work. It might, because SDXC is identical to SDHC in all but its file system, so the only thing would be if the 3DS is capable of dealing with its file system, which I don't know.
edit: it can, so if you want to buy one of these monsters
it will work, according to this:
but only if you reformat the card to FAT32, which is pretty easy, and you can google it
Usually sandisk has reliable SD cards, lexar is okay while currently selling the huge 128gig ones.
I dunno about transferring files however. It depends on how 3DS stores them, but usually you can't mess around with them once they are on the SD card.