There are differences of opinion on whether the filter should be after the tank or between the pump and the tank. If the filter is after the tank you sacrifice some pressure at higher flow rates.
If the filter is before the tank, then you need to assure that the filter gets changed. Also, you need to put a relief valve before the filter if you have a submersible pump, and maybe a second pressure switch with a bit of refinement of the control circuit.
You should find out if the sediment is coming from the well or if it is being precipitated in the water heater. If you have hard water then there is a good chance that it is precipitate. One way to check that is to see if the material will dissolve in vinegar. If it is sand it won't dissolve. If it is carbonate or calcium sulfate such as you get in a teakettle with hard water, then it will dissolve with warm vinegar.
If you put in a filter, then I recommend a large filter, such as the double length "big blue" size which is 4.5" diameter and 20 inches long. You would need pressure gauges on the inlet and outlet of the filter.