First, when in doubt: ask your fishmonger!
Whole fish can seem intimidating, but it can be very easy to cook. The easiest method is roasting, as described in the recipe for Roasted Redfish. Any size fish can be roasted whole, but 1- to 4-pound fish are ideal for home cooking. Have your fishmonger gut and scale the fish for you. Cut diagonal slashes in the fish if you wish (this gives you a great way to peek at the doneness as it’s cooking). Stuff the fish with aromatics like herbs and citrus. Roast on an oiled baking sheet at high heat (425°) until cook through, about 10 minutes per inch thickness (measure the thickest part of the fish).
Skin-on fillets are best cooked by pan-searing, pan-roasting, or grilling. Pan-searing is the best approach for fillets under ¾ inch in thickness. See Chef Schrier’s technique in the Sea Bass recipe for this method. Pan-roasting is best for thicker fillets (¾ to 1 inch-thick) starts the same way as pan-searing. Dry your fillets, season then and lay them into a hot, oiled skillet. Press the skin down onto the skillet to crisp it. After a few minutes, the fillets will start to turn opaque on the edges. Put you skillet directly into a preheated 425° oven for 8-10 minutes, until cooked through.
Skin-on fillets can stick to your grill. Two tricks that work well for us: make sure your grill is medium-hot before adding your oiled fish fillets to the it. Mayonnaise makes a non-traditional, but effective, non-stick surface for your fish. Rub the skin side of the fish with the mayonnaise and put the fillets skin side down on the grill. Cover the grill, and cook, without turning the fillets over, until cooked through.
Skinless fillets can be cooked by either of the pan cooking methods described above and can also be baked or steamed. To bake, lay your fillets in a baking dish and top with a seasoned crumb or herb topping. Bake in a preheated 375° oven until cooked through, about 10-15 minutes, depending on the thickness of the fish fillets.
Steam skinless fillets over simmering water or fish stock. Your fillets will take 10 minutes per inch (sense a theme here?). If you are steaming very tender fillets, wrap them in Swiss chard, lettuce leaves or another tender green before steaming.