Try to remember that utility trumps most considerations.
If the bag is too small to carry everything needed then it's an inappropriate tool for the job; a lunchbox, a warm jacket, a reader, a hat and scarf aren't heavy, but they are bulky. A small bag may be too small to contain the dimensions of your child's reader without folding it, which will make you unpopular with the school.
If the bag has wheels, remember that you child is going to be walking to and from school hundreds of times a year, so investigate the repairability/replacability of the wheels; a wheeled bag that doesn't roll is still a bag, but probably one that doesn't work anywhere near as well as a backpack. If you're not walking to school, what does it matter? A kid can lug any random bag 10 metres to the car.
Our school sells a school-branded bag, and its design seems influenced by the demands placed on it by the school. It seemed stupidly large when we first bought it, but it's got all the compartments that are helpful for storing things securely, and a few extra pockets here and there suitable for things like handkerchiefs, spectacles, dice (don't ask) and drink bottles. If your school does the same thing, it could well be worth your while to acquire one.