Bill Cody is the real expert here so I would always listen to what he has to say first.

I have a shallow one acre pond that I have played with and let it morph into different kinds of ponds. The latest morph pond it letting it grow naturally for my photograph of nature. A shallow pond grows lots of plants because sunlight reaches the bottom of the pond. So you have to control plants and algae. Some use chemicals to do this, (expensive), some use dye to shade the sun from penetrating the water and growing plants. and some use fish etc. to do the job.

Tilapia may be an easier answer then I have but must be replaced every year in Indiana. What worked for me in a one acre shallow pond was 18 grass carp for weed control. 20 KOI & 6 Israeli Carp for algae control along with frogs which produce algae eating tadpoles, and snails that also eat algae. Then for water filter I had clams. My other fish were Bass, Bluegill, Channel catfish. Bill Cody also said that crawfish could denude a pond of plants and I am considering experimenting with them this year.