Let me start this post off with a disclaimer. I know this suggestion won't work for every person but if I had my parenting years to live over, this is one thing I would do differently. I would take each of my children 1:1 with me as a mommy/child outing to do school supply shopping. School supply shopping was quite stressful as I remember. Here is how it went.
The older children were running through the school supply section with a list while I was trying to involve my youngest in the process of finding his supplies. There were always items we couldn't find until we went to the third store. Red checking pencils always required a visit to the office supply store.
There were the sometimes heated discussions about backpacks, lunch boxes and all the reasons that we should or should not recycle last year's pencil box. After all of that, no one was very happy, especially me!
I saw a friend recently and she told me she was out on a school shopping date with her youngest. They went out for lunch and then off to buy supplies. She told me it is relaxed this way and she gets to spend time 1 on 1 with each of her children. It's not as efficient as getting it all done at once. It sounds like it would be much better relationally and it would be lot less anxiety producing. You might want to give it a try for a new back to school tradition!