Apistogrammas are a bit harder to find in shops than many other fish. They can be a bit hard to care for so they are not a staple of the average LFS. Zebra danios are very active fish that do well in large groups although 5 is often enough in a small tank. Tiger barbs are very active fish also, and tend to be a bit too aggressive for many tanks. Although their water needs are much like the water needs for neons, they are not good tank mates for the relatively peaceful neons. Their normal nippy behavior, with being quite a bit larger fish, makes them a threat to the neons. Neons are great fish for many tanks although with long finned slow moving fish people sometimes have a problem with them being too nippy. They are also very small at full growth so they are often seen as food by larger fish like angels. The neons would go well with the zebras. You might want to avoid the tiger barbs and go with something else like rasboras or rummy nose tetras. You numbers do look fine so far but a different centerpiece fish is probably a good idea,unless you would like to increase your neon numbers to make them more the focus of the tank. There are also fish called black neons that get a bit bigger than regular neons and would go well in your small tank.
Do you also want to have some fish that are bottom dwellers like corydoras? They are also best kept in numbers of 5 or more and are not the sedentary fish that some people consider them if they are kept in larger numbers.