The Neon tetra is one of the most popular fish species among beginner aquarists since they are small, adaptable, cheap and easy to care for. If you are a fairly inexperienced aquarists interested in breeding fish, you should however avoid many of the popular beginner species since quite a few of them are pretty hard to raise in captivity. The Neon tetra is for instance really tricky to breed and a majority of the fishes in the aquarium trade are still wild caught, not captive bred.
If you want to try breeding fish, you can instead opt for one of the many cichlid species that are known to readily breed in captiviyt. You should however keep in mind that many cichlids are too aggressive for most beginner aquarist. The Black convict cichlid (Cryptoheros nigrofasciatus) is a great choice if you want to breed fish, since is easy to breed in readily spawns in captivity, but it is also a very aggressive fish. Another example of a cichlid that is easy to breed but somewhat difficult to handle due to its aggressive temperament is the Texas cichlid (Herichthys cyanoguttatus).
One of the additional benefits of picking cichlids is that many of them exhibit really interesting rearing behaviours. Livebearers tend to give birth to a fry and then simply ignore it, or even devour it. Cichlids on the other hand are famous for caring for their young until they are big enough to make it on their own.