It’s very localised op.
What would your dd prefer? Both rucksacks and totes are mostly fine in all the secondary schools around here as long as basic (am taking info from 4 schools). But the more ‘popular’ girls use totes in my experience. So you could get either as your dd prefers or both if you can afford it and presume both will be used. So a plain black rucksack, preferable Nike if not Adidas that can be used by others in the family and a cheap tote bag from primark - best to stick to black.
If you buy both and are able to drop her off on the first day, you could sit in the car and see what most girls are taking and have her take the bag, which blends in the most, bung her stuff in the chosen bag and take the other one back to the shop. My dd started with a rucksack and had a tote within about 2 days.
As for shoes, this is dependent on the school. If the school allows trainers almost everyone will be in trainers. They usually have to be triple black, which means the logo must also be black. Nike is best… or at least seemed to be for lower years. My dd’s former school allowed triple black trainers but not docs or kickers. Her current school allows neither and they have to wear ballet pumps or lace ups. Some of the girls start off in lace ups in lower years and by year 9 most are in ballet pumps, all pumps by year 10.
For PE you’ll probably have to get the kit. But the girls wherever possible tend to wear Nike pros.
As for coats, you don’t have to buy one now. You can wait and see what is in vogue. Dd is obsessed with coats and I told dd after I bought her last one (a Canada Goose) she would be funding any further coats so she bought herself a north face (no hood) on vinted.
I wouldn’t buy a lunch box or food flask. Not many kids use them even if some on this thread use them.
My dd is likely autistic (she’s 16) and the masking has been phenomenal despite my having suspicions at times and being told I’m wrong… and now finally told yes, she likely is but cannot be diagnosed just yet… She is absolutely obsessed with fitting in. Has to be exactly the same as everyone else with anxiety through the roof. So I totally understand the anxiety and school refusal, having to have the right shoes, bag, coat etc. We had a lot of that when dd was in primary and I ended up not buying her school shoes until she’d started the autumn term so that I could buy the same shoes as her friends. Transitions were particularly difficult.
Good luck with your dd. Give her a big hug if she will let you. It’s hard.