There is no such thing as a "perfect" aquarium for your fish. Animals need different environments so each aquarium will be a little different depending on what animals you have. Oftern times this just mean having the right accessories in your aquarium.
You need to first decide what fish species you want. For example there are some differences between saltwater and fresh water aquariums. Saltwater aquarium have become popoular recently because of the unique species that can be added to them.
You also need to make sure you have the right size aquarium. Ask at your local pet store when you purchase a fish what size of tank you'll need for it; You should also know about how many fish you want to keep.
While some pet stores tend towards cramming large numbers of fish into a relatively tiny tank, keep in mind that this is because they are there for display purposes, and that those fish are sold off quickly so comfort isn't much of a priority. You need to have a enough space for your fish over the long term.
You need to also keep in mind that some breed are very terrirorial and get get agressive.
Generally tanks will have at least 20 gallons. Along with water capacity, you should also keep tank shape in mind... Some tanks will be wider then others for example.
Your tank will also require a filter. Filters keep the tank filled with oxygen and also clean. Wet/dry filters with pumps are the most commonly used for aquariums, and these keep the water circulating constantly. These types of filters are also low cost and easily maintainable.
Gravel filters are also common. They cost more and harder to maintain also allow for biological filtration.
Corals and other living filters can also be grown in trays. while these are commonly used on full fish ponds, miniaturized versions are available for some larger aquariums. Biological filters are the most efficient and natural.
The third type is also more common for salt water tanks. There is also an entire ecological system involving ammonia and nitrogen that keeps salt water fish alive, and that requires biological components like marine plants to keep the cycle going. The cycle within the salt aquarium is better maintained with a bio filter.
Your tank will also need a heating system. Some fish are much more sensitive to temperature then others. Tropical fish, in particular, will need to have an aquarium with a heater, especially when taken to a colder climate. but no mater what kind of fish you have heating systems are still important.
An aquarium starter kit is one way to easily get started without stress.