Ignore the R4 carts unless you want to have to patch every protected game (most of the newer games are protected) compatibility is also lower than other fash kits & there are alot of fake R4 carts that are even less compatible, if you do get one of these though, the 3rd party flash kit software R4Wood is recomended to use if your version of the R4 works with it (with the fakes alot of those will not work with R4Wood)
The Acekard2i is one of the best and yeah it plays NDS roms just fine on the 3DS
The Acekard2i has the best compat for NDS games without patching the roms
The only issue is that most of these flash kits will need updating to work on the latest version of the 3DS
other cards that are worth note
the Supercard DSTWOi is also a very good kit though a lil more expensive it aso has support for SNES and GBA via emulation and has extra memory in the flash kit to enable this (compat for the emulation aspects are not 100% though, but still very good)
Updates if the shop you are buying from don't do this for you, is done via a NDSlite or original NDS (This is the downside to any of these flash kits on the 3DS), future updates can normally done via the 3DS before you update the 3DS itself