It is true that most of the work should be done before you even get started. You need to do your research well to make sure you get all the right stuff before you buy anything at all. Only after everything is set up, you can do aquarium nitrogen cycle. The fish should not be brought home until your aquarium filter is cycled.
While it is possible to have your fish in a smaller than minimal recommended tank, there is no way you can use a filter that is rated below the minimum requirements. You can certainly use a filter designed for 40+ gallon tank on a 10 gallon tank, then the current will be too strong for the fish in that little 10 gallon fish tank.
