In terms of stocking up, it really also depends as others have said what your set up is. If you have a garage or under the bed space, by all means, it never hurts to have some extra trackies and shoes you saw on sale in a size or two bigger in a box for whenever the inevitable growth spurt cames on. I'm also a charity shop fan- easy come, easy go, but it requires a bit more of a long term view of what the kids need and the ability to store stuff.
Ours both came with loads of stuff. On their move in day, and for weeks afterwards we had bags and bags of toys and clothes and memory boxes that we really struggled with because we didn't quite know what was important and what was just... stuff. It shifted our focus from the kids to the stuff, and they had to play around it.
If you are asking for advice about what not to buy, I have plenty 🤣 consider me a deinfluencer! (Usual pre emptive caveat that this worked for us but other people might disagree!)
Ours were 2 and 3 when they came to us. The stuff we didn't bother with, or wish we hadn't included:
Jigsaws and things with small pieces (absolute bloody nightmare when they are tipped over), increased our stress levels no end. One or two, fine, but ours ended up getting all the pieces confused.
Basic "under" clothes (before you get them)- once they get confortable with you, they might start working out that they don't like certain textures or materials, or just that they prefer certain cartoon characters for example.
Smart wear. For some reason I bought several light coloured chinos and shirts for my children as though they would be attending a summer garden party every day. We all dossed around in trackies for 98% of the time!
Cot beds if they are on the cusp. we just ended up going straight to a toddler bed. Ditto bedding sets etc.
Toys in general. You end up picking up toys from everywhere, people give them to you, you can get them for a couple of quid from charity shops, Christmas, birthdays etc. Most kids don't need a tonne of toys, and it can be a bit overwhelming to know what to play with. You also want your focus to be on playing with them, not choosing or tidying toys.
Too much of anything consumable in the stage the child is currently at. So for example, weaning foods, bath products, etc. firstly they will grow, but secondly it might not actually suit your needs. We bulk bought a load of rusks at the FC advice only to find it was unnecessary and we were left with a load of them.
Nappies and pull ups, unless you are confident with the brand. Ours came in pampers, but when they were still leaking. we switched to Aldi own brand and they fit them so much better. We had to go through several weeks worth of pampers first though.
Things I would suggest "stocking up" on:
Your own medication-sort out a few months supply from the pharmacy if you can.
Painkillers and general first aid stuff for both kids and you (plasters are a great visible way of soothing all sorts of ailments, Calpol and ibuprofen because it's a time of huge stress so the child is probably going to be sick at some point in the first few weeks!)
Checking any subscriptions that might be going out of date and cancelling or pre renewing.
Your own toiletries -shampoo and conditioner
Easy cook and air fryer goods. The best present my mother ever bought me was my air fryer and it got used ever single day for fish fingers and chips for the eldest.
Washing powder
Spare shoes for the car/nursery. We always keep an eye out for cheap or charity shop shoes to bung in the boot of the car or nursery bag so that we don't have to stress about wet feet.
Spare trainers, shoes and wellies for yourself. Mine took a battering!
Outdoor wear. We always have spare coats and waterproof trousers because the kids are outdoors kids and they get them wet and grow out of them. I prefer bright colours so that I can see them in the park if at all possible, and depending on the trends in the shop at the time, they might be harder to find. We have a main coat, a coat for nursery and/or dirty wear and a coat for best. Oh
School uniform- I'm forever on the look out for school uniform bits and pieces in the 50p bin at charity shops because goodness me we go through school trousers and jumpers at a rate of knots!