First of all, have you let the tank cycle?
http://www.fishlore.com/NitrogenCycle.htm
If not, I would go through that before buying any more fish. As you've already added fish, follow the "with fish" section.
Do the fish in this article
http://www.fishlore.com/profiles_glowlight_tetra.htm
look like what you have? If so, they'd probably do best with two more of their kind as friends.
Presuming this is the case, that puts 10 fish at about 1.5 inches per fish in the tank. That's 15 inches of fish. You'll want to top out at around 28 inches of
adult fish (one inch per gallon, which ceases to work when you're dealing with larger fish, but with the kinds of fish you're looking at, it will work fine) In my opinion, a single mystery snail wouldn't be a bad thing. Figure it takes up another two or three inches (they produce quite a bit of waste). That leaves you with about 10" worth of fish left.
As the neons and (presumed) glowlights stick around the middle to the bottom of the tank, it might be nice to have something going on toward the top of the tank. Guppies would be excellent for this. They would probably be my first choice for your aquarium, as they're hardy, colorful (important to kids), and peaceful, so your neons probably aren't in any danger from them.
One note if you're going to get guppies: If you get males and females, be ready to teach your kid the facts of life and death. They will breed, and they will probably eat their babies. Guppies make about the worst parents there are (of course, in the wild, there's much more room for the babies to escape).
This could be an excellent learning experience or it could be a parent's nightmare. If you think it would be the latter with your kid, just get males (they're the more colorful of the genders, and are really easy to pick out. Petsmart usually has them separated by gender anyway).