When purchasing an aquarium you will need to think about its size. This is a very simple process. The bigger the better because the greater the volume of water the more stable the water conditions will be depending on fish stock levels.
A small aquarium holding a small amount of water will fluctuate more in terms of water chemistry than a larger aquarium. If for example a fish dies in a small aquarium then the water chemistry can quickly change with ammonia levels rising quickly. In a large aquarium the dead fish would not pose so much of a problem because the beneficial bacteria inside the aquarium will be able to deal with the excess ammonia better plus the ammonia will be diluted in a much larger volume of water.
However it is not just about water volume. Ideally you want a tank which will have a large water surface area to allow the air to come into contact with as much water as possible. This will help to keep the aquarium oxygenated. A tall aquarium with a small water surface is a bad choice because the water will quickly become depleted of dissolved oxygen.
It is becoming increasingly popular especially for reef aquariums to have a shallow aquarium that is deep and wide. This allows good oxygen exchange, less light is lost as it travels to the bottom of the tank and the water volume is still large creating more stable water conditions. Obviously this type of aquarium will take up much more room but is worth thinking about.
Some people may actually want to have a tall aquarium so that they can plant tall plants and in such cases air stones can be added to disrupt the water surface helping to add dissolved oxygen into the tank.
In general and if you are not going for a fancy design most aquariums will have been built with these parameters in mind.
There are formulas to work out aquarium water volume and fish stocking levels but remember that when you add rock, substrate, ornaments, power heads, heaters etc that these will all take away from the water volume. A large rock display popular in Cichlid tanks will take a lot of the water volume away.