Filter After Pump?

I am planning an inlet filter, first flush diverter system and inlet screen to filter the water going into my storage tank. After all of the filtering that will be done before getting the water into the water storage butt, do I still need to filter the water between the pump and the header tank? The water will be used for WC flushing, washing machine, showering etc... It will not be required as drinking water.

If I do need to filter the water again, do the filters have a specific name?

Thanks for replies.

Elliott