What kind of fish are you looking for, and are you thinking of cold water fish, or tropical fish?
Just like there's more to a dog than letting it pee and poo on short walks, followed by a game of fetch, there's more to keeping goldfish than a simple round bowl.
The lowest care fish are bettas, which are Japanese fighting fish. No more than one to a small bowl (they're puddle dwellers, like murkier water, and it can be small and shallow)
Goldfish require much more care than a simple bowl - they are one of the dirtiest fish around, and in regular glass bowls they live no more than a year or two if the water is changed every few days - because they poison themselves with their excrement. Goldfish are carp and can live to be 15 years old if they are one to a 5 gallon tank complete with water filters and proper water cycling (water cycling is a learning curve in and of itself).
If you want anything more than an easy care betta, you'll need
at least a 5 gallon tank, a water filter (the strength of the filter depends on the fish you're going to keep), a thermometer, dechlorinator, and if you've got tropical fish, a heating device.
If you go for goldfish and want to keep them physically optimally healthy, you will likely need to upgrade the tank from 5 to 10 or 15 gallons (depending on how many you're keeping) after 5 years. The more goldfish you have, the stronger the water filter needs to be. For example, a 5 gallon tank, with 2 goldfish, requires proper cycling AND a 10 gallon water filter, and an upgrade to a 10 gallon tank with a 20 gallon filter in about 5 years. Anything less than that will cause physical strain on the goldfish.
With tropical fish, they tend to grow less, and are less self-soiling. You can have more to a tank, but they still require a good comprehension of cycling.
Here's a pretty decent explanation of the first steps toward getting started on any kind of tank:
http://www.firsttankguide.net/steps.php
And here's a brief explanation of 'cycling':
http://www.firsttankguide.net/cycle.php