If your tank is not heavily stocked with critters, an air pump/sponge filter will be fine. I've got a 30 gallon tank with 1 axolotl, and don't have much of a problem (other than the brown algae, which is a constant battle).
You'll still need to do regular water changes, sometimes a bit more.
If you have a cycled tank, just take the old filter out and plunk the new filter in (after you wash it thoroughly to remove any shipping debris). The bacteria will seed the filter very quickly.