This is my take on more complicated Russian fish soup.
I buy heads and carcass/bones, or some cheap fish like whole tilapia, but make sure there are bones in it. Bones is what will give you the rich broth. Cook in a pot like as if you are making meat stock. When you think it is ready, strain the broth, discard the bones. Now add some chopped onion, potatoes, carrots, black peppercorn, bay leaves. Salt/pepper to taste. When it is close to be ready, I add chunk of salmon, or halibut, white fish is also fine, but I would recommend fillets. Add fresh dill and parsley. Cook until the fish is just done, do not over cook. Separately cook barely or rice, whichever you like better, add a spoon or two to the bowl when serving.