If your not a complete klux and hamfisted then the best first stage is to use a window scraper (such as
https://www.toolstation.com/stanley...9-pBG4xCApIRIFNaAnhoCUjYQAvD_BwE&gclsrc=aw.ds)
Draw/pull it slowly
down the screen (backwards in effect) and a high percentage of the scum/water hardness will just flake off, its the temporary hardness and its not that hard in effect
Then you will find it far more efficient to use a product such as viakal as its only working on a small volume of stuff you want to remove not trying to dissolve large amounts
you can even do it directly with a stanley blade but the scraper makes it easier to get the correct balance of pressure
Note this is for glass screens.
As others mentioned, wiping/squeeging down frequently will help reduce the build up. As the water dries it leaves the marks, as they build up a larger and larger quantity of water can reside, vicious circle