There are several types of small aquarium fish that do better in the smaller environment. Here are a few that are great for starters.
Tetras are great small aquarium fish due to their like of cold water. They are best in a small school.
A guppy is a very small fish, and also does well in colder water
A platy is a very colorful fish, and it also adapts well to various small aquarium environments.
The Danio is a very hardy small aquarium fish.