Baking powder, especially if too great a quantity is used, adds an unpleasant flavor to a baked good. Even in an appropriate quantity it can be noticeable and it certainly doesn't do anything to enhance the flavor. Many baked goods traditionally don't use a chemical leavener at all, but instead rely on technique. Creaming butter and sugar together or whipping egg whites was historically used to make cakes which rose solely based on the bubble network that was created.
Yeast, on the other hand, creates a delightful flavor that you associate with your favorite crusty loaf of bread. Yeast can be used not only in making bread but also in some excellent cakes (St. Louis Gooey Butter Cake, for example, although many "knock off" recipes cheat here and miss out on the true goodness). Yeast also provides a significantly different texture during the rising due to the intentional creation of a gluten network (usually something you absolutely don't want in a quick bread or quick cake) — you don't get a crumb with big, airy holes from baking powder or baking soda with an acid.
Also, in my experience baking powder lasts six months in the pantry and yeast lasts at least six months in the fridge. The shelf life is not so different.
If yeast scares you, you may want to check out some of the proponents of the no-knead bread technique.
For a lot more information on this subject, there is a recent publication that covers all sorts of leavening agents.
To answer your main question, you can bake very just about any type of fish.
Looking at that recipe though, down in the "tips" section, it suggests you use a flaky white fish. So in that category, you have lots of options, snapper, cod, tilapia, for starters. Their flavours are often a little more mild and will pair nicely with the tomatoes and other flavours in there.
If you're prone to overcooking it, take it out sooner. I find many fish recipes that give cooking times tend to get you to overcook it. It'd done as soon as the fish "flakes" fully. Leave it any longer it will start to toughen quickly.
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All I've been able to find is that is a novelty name for a baton tray, this could be wrong but I've found no other tray called a "Wingy".
That or it could have been a typo in the recipe.