Beginning with is it from a well or a municipal system, the water experts here will likely want to know more about your water before making any detailed recommendations. In my own case, my water softener needs a sediment filter in front of it, and that filter helps to keep my aerators clear at the sinks. Other than that, my water softener does whatever it does to my well water for whatever reason my wife appreciates!
Oh, and especially if you have a septic tank and/or drain field of your own, the discharge from your washing machine should be filtered for lint removal. Over time, that lint can plug up a drain field.