There really are lots of choices out there, it is just overwhelming. I don't know anything about the corn by-products, but as far as corn syrup and high fructose corn syrup, I don't bring it into the house by choice. What kinds of foods are you most concerned about? Snacks? Sweets? Meal foods? Here are some things that are in my house regularly that I think fit your criteria:
-Organic or "Real" Foods: lots of supermarkets, including meijer, have a decent selection. I use their ketsup all the time, they have things like animal crackers, graham crackers, goldfish, waffles. You can find lots of flavors of jams and jellies, peanut or almond butter. There are lots of organic or all natural cereals out there too, but those will be tougher for you because of the corn products. Chocolate free of corn syrup does exist, it's just a little pricey. There are organic brownie mixes (or it's easy to do from scratch with a can of cocoa powder. I've seen organic chocolate chips, meaning it is still possible to make homemade chocolate chip cookies!
-fruits, veggies and dairy: my 3.5 yr old DS goes in fruit phases. Sometimes he carries a dish of green grapes with him everywhere, other times it's a plate of apple slices. He also loves strawberries, kiwi, starfruit, pineapple, watermelon, banana and cantalope. Mott makes a No Sugar Added apple sauce that is free of corn syrups and fake sugars. Currently, my DS won't touch veggies, but think about a dish of red pepper slices, baby carrots, pieces of celery, cherry or grape tomatoes or cucumber. I'd be lost without cheese sticks, cottage cheese and a weekly staple at my house: Dannon All Natural Lowfat Vanilla Yogurt. My kid eats this stuff every day and loves to dip his graham crackers in it.
-Home Made: As tough as it is with a preschooler and a baby, you know what's in it when you make it. French toast or pancakes with real maple syrup (not the brown, butter- flavored high fructose corn syrup junk). There are pre-made crusts out there that are all natural (or box mix) so you can make your own pizza. Home made mac & cheese isn't much more effort than making spaghetti (lots of sauce options for pasta). Popcorn sprinkled with parmesan cheese is a favorite snack. Unfortunately, both brands of flour tortillas I use have corn starch in them (chi-chi's brand and Tortilla factory), but you may be able to find some without it in the organic dept. If you can, you're open to tacos, and quesidillas and one of our almost daily meals here is a grilled cheese made by putting cheddar cheese in a tortilla with a couple pieces of honey roasted deli turkey rolled up and toasted on my george foreman grill. (I buy hormel all natural deli meat-it has no nitrate/nitrites and is available in presliced/prepackaged part of the meat cooler near the cheese-they also do ham and roast beef). I make a super yummy cream cheese frosting for cakes (butter, cream cheese and powdered sugar). I've done it strawberry by adding pureed frozed strawberries, or chocolate by adding cocoa powder.
Sorry this is so long, but I hope that it gives you some ideas or at least gets your imagination moving to think up things that will work for your family. I'll bet the hardest part will just be changing your habits here at the start. Once you find alternatives for things you are used to having it will be easy and all of you will be healthier.
Good luck!
C., Battle Creek