All three types are recommended, but an aquarium needs to have at least biological and mechanical.

 Components of these media types can be incorporated in the same filter. 

The three types of filtration utilize three different types of media to perform their functions

Mechanical media

The components of mechanical media are inert - this means they will do nothing to interfere with your water chemistry such as a sponge. This media mechanically or physically strains solids from water passing through it, which is important to the efficiency of your biological media. Mechanical filtration removes unwanted particles.

 To prevent build-up, the filter media must be cleaned regularly. 

Biological media

Biological media is anything inert such as lava that provides housing for beneficial bacteria that break down dissolved solids to a less toxic form. This is a media that should not be replaced unless it has become too clogged to function

Chemical media

Chemical media is not used as often as biological or mechanical media, but can be effective for an assortment of filtering purposes. This media is available in a variety of materials that can remove one impurity or many.

The chemical method of filtration removes dissolved particulates from the aquarium via activated carbons, resins, and other adsorbents. Chemical filtration media helps to maintain water quality as unwanted dissolved matter adheres to it. The two most popular forms of chemical media are activated carbon and resins. Protein foam skimming or oxidation with ozone are two other forms of chemical filtration