designing the water filter depends on the initial water quality (inlet) and required domestic usage. if intended for drinking you have to be carful and consider to have a water free from pathogenic.

However, for other domestic purposes gravity filter is capable to fulfill the required water quality. for instance, use sand filter with support layer of zeolite (tuff) is good cost efficient choice. also you can use anthracite or activated carbon as a top layer to improve the quality of filtered water

Potable water production, even in a household scale, requires to follow up the esencial steps for treatment plant designs.

The source water quality will define the treatment proceses you need, as well as the local standards (regulation) as a minimum target for water quality.

If you are considering 'potable water' as 'drinking water', then I suggest to use international standards to produce a healthy and acceptable organoleptic drinking water.

A first step of filtration with sand, anthracite or zeolite es mandatory, followed by an activated carbon (GAC) filter step.

If the source water contains iron or manganese, add a greensand step.

If the hardness is higher than 500 mg/l, a softener will be required.

Finally, a disinfection to assure the virus, bacteria and pathogens elimination si mandatory. You may include a UV system before a chlorine dosage.

If you want to produce high quality drinking water, you may add a Low Pressure Reverse Osmosis small system that may include a post filtration with Carbon Block and a final UV desinfection.