"The term dither fish refers to an arbitrary group of aquarium fish used by cichlid keeping aquarists to reduce innate timidity in some species of cichlids.[1]. Dither fish typically swim around the top of a tank and this behavior encourages more timid fish to relax and venture out more by reassuring them no predators are around. The technique relies on the ability of cichlids in an aquarium to use the behaviour of other fish species as a measure of environmental security.[2] Good dither fish are typically schooling species, such as some Danio species, barbs and some tetra species." -- Wikipedia
In terms of the tetras, a lot depends on your filtration and decor. If you have good filtration and a nice combination of heavily planted areas and open space I'd say you could probably do 8-10 rummy nose and 8-10 cardinals. For the GBRs, remember that your tank has to be very well established in order for them to do ok. Rummy nose and cardinals are also very sensitive when first acclimating them, but I've found that the most important thing for these sensitive sort of fish is to make sure you get them from a reputable breeder or LFS where you know they're being treated properly.
