Good for you for doing something you dislike because you know it'll benefit your daughter. Way to go, mama!
Personally, I'm a big fish and seafood lover. I'm not sure I can answer your question about types of fish that are safe for babies but, for now, it's probably better to stay away from tuna and swordfish because of mercury concerns.
Fish doesn't keep quite as long as beef or chicken. Buy the thickest piece you can to avoid drying as it cooks (it takes a while to develop a touch in cooking fish and many people new to cooking it tend to overdo). And, yes, it's perfectly OK to refrigerate and re-heat later. I do it all the time.
For flaky white fish like cod or haddock: place it in a baking dish (skin side down, if it has skin), sprinkle with some bread crumbs as you like (I like fewer, my husband likes more), dot with butter. Add a little thyme, salt and pepper and maybe a little lemon juice. Bake in a 350 oven for about 20 minutes or until done (it'll be flaky when it's cooked through).
For heartier fish like salmon (and later for tuna and swordfish): brush with a little olive oil or butter (olive oil smokes less), sprinkle a little lemon juice and broil.
Piece of cake! and quite yummy.
I don't think fish sticks are the healthiest option, kind of like chicken nuggets versus broiled or roasted chicken, put probably not terrible on occasion. I like 'em with tartar sauce, myself.
Have some fun experimenting. Who knows, you might find something you like, as well!