Anything you can eat at home, you'll be able to eat at Disney. Just watch the quantity! I find it more cost-effective to order from appetizer menus, although those portions are often too large for me to finish. I'm never going to get my money's worth, but I've lost 110 pounds. I'm good with that!
ETA: People often suggest ordering from the kids menu, which is fine if that's how you want to eat. I'm on vacation, I'm not ordering a kid's quick service meal to enjoy a small Dannon yogurt drink and a Cutie, but YMMV.