If you will just be happy to play NDS backups and aren't bothered about other stuff you should get the "R4DS" or "M3 Simply". These are both cartridges which slot into the DS. They hold a micro sd memory card which is used to store the games and typically a Gb card stores about 20 games average, 2Gb, 40 games etc. Total cost about £40-£50 total (60-75 Euros or $80-$100).
some games are about 32/64 Mb's each however you can trim these to get rid of varying amounts of memory.