you have around a 15 gallon tank.
you should have really done a fishless cycle.. but w.e your call.
what i would do, after your tank is done cycling.
up the number of neons to 6+ that are a schooling fish.
you can get peppered cories for the bottom.. they like sand the best and need small non sharp substrate.
and a show fish can be a beta.
then in a few months you can bump your tetras to 10-12 which will give a very nice shoal.... leave the cories at 6 and a moon beta (my favourite) will complete it... also if you choose to do a heavily planted tank you can throw in some cherry shrimp.. or have a colony of shrimp around 10-20 and not have cories.. then combining with a rock shrimp.
for fish for the top you can get cloud tetra.. they are very nice and stay near the top.. remember to have schooling fish always in groups of 6 and try not to over stock your tank.. or bump up the weekly water changes.