I suggest the "poor man's neon tetra" as tankmates. If your girlfriend likes it it should probably stay. Goldfish are pretty good fish, but they can be real trouble sometimes. THey are probably one of the worst fish for beginners. They eat plants, they grow large, they like cold water, their fins are tempting for nippers... At least they have a cute face, and they pay attention to you when you enter the room by biting the glass and cruising around the front in circles...
"poor man's neon tetra" is of course the white cloud mountain minnow. They are small, active, twitchy and often display to one another. (which mind you, is interesting to watch)They actually do look like neon tetras from a short distance, the young have dark body with red fins and the stripe is very blue. The eyes are blue and the dorsal fin and anal fin are much larger than they look, plus they have yellow rims.
The WCMM rules! You could fit about 10-15 in that 20 gallon tank with the goldfish. They stay small so they would have enough room to make a good school. I have not observed a good school though. I had too few in too large a space and they just spread out and cruised around in trios or pairs. The goldfish should get large enough to intimidate them into better schooling.
GOOD LUCK with your TANK. I suggest uploading your photos to photobucket and posting links. They will work almost no matter what that way.