Okay so you want clear water and no muck in a pond that has 20 years of muck and I suppose, a lot of fish? Do you want it tomorrow? Sorry, i’m Trying for humor here but am not good at it. We need to know how many fish and how much food you add to the water daily. That will tell us how much daily muck is produced by your school. Then we can talk about filtration size and total water flow. Theoretically you need to turn your pond volume over once every one to two hours through filtration designed to service a specific weight of fish. With that information we can plan to remove the weekly amount of waste your fish produce so that the pond never builds up muck again. The pond should draw water to the filters from both the bottom and top surface. Bottom drains and top skimmers. The filtration can be pressure filters, bog filters or a combination of both. The main point is that muck buildup is controlled when the pond removes 100 percent of the solid and chemical waste produced every day through filtration.
As for the green algae problem the question is how much visibility do you want? Crystal clear or visible down to a certain level? That is your choice and drives your choice of mechanicals. For our pond for example we are happy if we have good visibility down to about 30 inches. We like some turbidity because the fish feel safer when they can hide a bit. And we can see them just fine when we feed. That concept tends to foil predators too. We have never had a heron death, and our pond is only about 30 miles from the second largest heron rookery in the United States.