It seems your desire is to save money. I don't really know in general about comparing online vs. at the store. It seems as though things like pencils would be cheaper at the store since no shipping is required, but if you are buying textbooks or other reusable items, online and used can be a great money saver.
In terms of saving money, I would also recommend As a former teacher, Most of the supplies a day or two After school has started (At least in the States). Often the lists are published by the administration and include things the teachers would never have actually included on the list and that your child will not use.
Make sure your child has a binder (or filer), pens, pencils, erasers that work and some paper and something to keep it all in. Generally the first day or two are orientation to the class and don't result in a lot of work anyway. These basics will get your child through that first day just fine. Then, find out what the Teacher wants by looking through the paperwork that comes home. I would also encourage looking for anything major like laptops (I've taught at private schools that Did require these) or specialty items and tools that are sometimes required in the secondary grades ahead of time.
The extra advantage? Not only will you save by not purchasing supplies that aren't really needed, you will also get to take advantage of the clearance bins at the stores or online.