Replacing the screens is easy.
Last year I started the process of replacing every screen in our house. They were the old aluminum/shiny style and absolutely filthy.
Just go down to your home improvement store and buy a roll of screen. You can buy good, better, or best. Higher price means easier to see through. Then you buy a cheap plastic tool, and some spline. It's all going to be in the same area, so easy to find.
When you take the screen frame out of the window, you'll see that the screen is held in place by the spline which runs all the way around in a groove. You'll use pliers to pull the spline out, throw it and the old screen away, wash down the dirty old frame. Then cut screen to fit, with several inches overhang all the way around. Then put the spline in one corner and start working your way around using the tool.
It takes a bit to figure out the best way to do it, but it's easy to figure out. I've never done it in my life and didn't find it complicated. You'll learn that you can't pull the screen too tight, or you'll twist the frame. If you don't pull it snug enough, your screen will have waves. You'll figure it out. Also, it is easy to pull on the overhanging screen to "pop" the spline back out of the groove, then tighten or loosen the screen and redo the spline.
I'm sure there's youtube videos that explain it far better.
But just wanted to assure you that it's an easy diy project and SO worth it. I replaced two screens on one side of my house and those windows looked night and day different from the street than the tired old screens. Amazing! Plus, SO much easier to see outside.
I'm looking forward to getting the rest of ours done this spring.