Particulates in well water

I need to install a particulate filter on my well water system. I have clean, safe, good-tasting water, but sediment builds up at all fixture screens and has repeatedly fouled my washing machine cold water valve. I'm seeking recommendations for an inexpensive filter I can install myself, and advice on whether to install it at the pressure tank, at the external cut-off valve, or inside the house.

Thanks,
John

What kind of sediment is it? It may not be sediment, it may be rust because there is iron in your water. Or hardness scale etc.. And if the water is clear, it won't be invisible dirt build up because that would go right through the hose screens and faucet tips.

It's definitely not iron. Most of the particles appear to be some form of calcium: white, brittle, rough-surfaced. The water is quite clear.

You need a water analysis for at least pH, hardness, iron, TDS, sulfates and chlorides.