selecting fish
How do you decide what fish to get, beyond just their looks? There are several points that can help you decide.
Lean towards freshwater fishes
Saltwater fishes are harder to keep, as water's salt-content (or salinity) must be maintained. That means that you can't just use conditioned tap-water. You have to add measured salts to it, and monitor that salinity with a hydrometer. Usually people buy marine water, and use that. Because you can use tapwater for freshwater aquariums (costs a fraction of a cent per gallon) and must use seawater for saltwater aquariums (costs around 25 cents per gallon), it is cheaper to invest in a protein skimmer (costs $50-100) to keep the saltwater clean rather than do frequent water changes. Saltwater fishes are much tougher to breed than freshwater fishes, which means they are often caught in the wild and sold. That makes them both more expensive, and less forgiving of water-chemistry problems. They also tend to be larger. If you are considering saltwater fish, you should really be thinking of a tank that is 100 gallons or larger. Freshwater fishes offer plenty of choice, and are really the way to go for a first-time fishkeeper.
Lean towards schooling and less-aggressive fishes
Schooling fish give you a chance to see social interaction between fishes, which is fun and enjoyable. On the other hand, you need to keep a certain minimum number of them which seems to reduce your variety in a limited tank space. However, non-schooling fish usually come with some anti-social habits, and you have to plan their tankmates carefully. If you put in a less aggressive fish with a more aggressive one, the less aggressive one will likely die from stress, injury or being eaten. Pick schoolers like Tetras, Platies and Mollies. Avoid Bettas and Cichlids. There are some loners with mellow temperaments too, such as Killifish, which are good. You should also be aware that some active smaller fish can stress out and sicken more mellow larger fish by their incessant sudden movements.
Don't be too quick to get goldfish
Goldfish are a big fish that become a foot long or longer. They get stunted and die prematurely in smaller tanks that aren't big enough. If you're going to keep 3 goldfish, plan a tank that's at least 55 gallons. They also prefer water that is too cold (65°F) for tropical fish, so keeping them limits your choices on which other fish you can keep. On balance, opt for smaller fish to start with.
Consider staying within a 5-inch maximum limit
Larger fish need more space and tend to be more expensive. There are other reasons to stay with smaller fish also. For one thing, big fish poop more and tend to be messier in the tank. For another, they can bully their smaller tankmates, and prevent them from feeding. If you plan on bigger fishes, be extra-careful about compatibility with other tankmates. As a new aquarium-keeper, lean towards fishes that are 5 inches or less when fully grown. If you mix fishes of different sizes, take care to provide shelters for the smaller ones where the larger fish cannot follow them.