I also agree that many of the answers below are good. I would only add this: there is no place for coco puffs and cookie crisp in a healthy diet. Why would you buy these in the first place? Buy healthy cereals, period. Don't have junk food in the house, and many of the battles will become a moot point.
I am ok with my daughter eating toast and butter for breakfast - we buy really healthy bread with no corn syrup, and it has all kinds of seeds and nuts in it, so I know she's getting at least some healthy nutrients.
I am considered a 'health food freak' by our kids... I do try to stick with fresh fruit, veggies, whole grains, etc. But I know everyone wants their treats and I'm ok with having treats provided they eat healthy meals and snacks. So here, we simply don't buy junk food, with the exception of maybe one thing - we might have one package of cookies in the house, or one container of ice cream, and that's it. Other than that, they'll have to find healthy foods for snacks after school, breakfast, etc. It may take your family some time to adjust, but I really encourage you to purge the junk out of the house, replace with healthy alternatives, and give it a try. (One tip - buy things like healthy trail mix (no salt, not loaded with chocolate chips, etc). Buy dried fruit, some different nuts, etc. Find new recipes and make new healthy meals or snacks if you need to. If you have new and different things for your family to try, that will help in the transition.)
One last thought... you mentioned your daughter will sometimes have toast with cheese. If she has that sometimes, but other times doesn't want the cheese, that doesn't sound so terrible to me. Not every body needs the same foods as everyone else, and we need different things at different times. If she doesn't want cheese on a given day, maybe it's fine to listen to her body and leave it alone. When she needs it, she'll ask for it. By the same token, if you feel like she's not getting good nutrition, offer an alternative. If my daughter won't eat something healthy for a meal (if she really hates what we are having, for example), sometimes I'll offer something totally different and she'll go for it - she's had breakfasts (and dinners, now that I think of it) that include pistachio nuts, avocado, carrot sticks, and other wacky things - but I know they are healthy so that's fine.