The answer depends on what kinds of fish you want, and whether you want a freshwater aquarium (which is typically considered easier to set up and maintain) or a saltwater aquarium.  You can find advice on eHow for selecting freshwater or saltwater fish, and setting up a freshwater or saltwater aquarium.

By the way, here's my personal favorite freshwater species -- the Siamese fighting fish.  Just don't put two male Siamese fighting fish in the same tank, because they really do fight ....