Firstly, stock up with a large cardboard box that others cannot see into and put it where the rest of the family won't raid it. I get a few extra things every week - but look out for special offers on the overall list too (usually get a lot of things over the next 16 weeks or so) so it will cost less too.
Back to school specials could be good for "lunch box essentials" like crisps, popcorn, mini-chocolate bars, multipacks of fizzy drink cans, etc. And perhaps other store cupboard items. There will also probably be special offers on sweets, choc coming up to Halloween.
Think about what your family likes to eat and use over the whole Christmas season - both festive treats and regular things you use more of because everyone is at home all day or because you host loads of guests. I don't buy everything I mention below, it's to get you thinking about options.
Food wise - do you like leftovers as curries or pasta dishes? So get a few extra bags of rice (do you prefer basmati rather than easicook at this time of year?) or pasta (IKEA do Reindeer shapes that can be fun!). Extra ingredients for these too - tins of tomatoes, coconut milk, dried herbs, spices blends, or jars of particular sauces that your family likes. And other stores items to whip up lunches or quick meals - tins of tuna fish, sweetcorn, sardines, salmon, Chinese bamboo shoots or water chestnuts; bottle of passatta, Chinese/Indian/Italian/Thai sauces, pack of fajita mix, salsa and some wraps, couscous, risotto rice. Condiments such as olive oil, vinegar, ketchup, mayonnaise, mustard, sugar, salt, pepper, stock cubes, corn flour (I use for white sauces)....
Do you bake? So an extra bag of flour, packet of sugar (different types like brown, castor, icing etc), dried or glace fruit (raisins, sultanas, currants, mixed peel, cherries etc), chocolate chips, other ingredients you'd use (including decorative things). Also snacks like rice cakes, dried fruit (mango, apple, etc), pots of fruit purees, etc that you or the family might eat.
Deserts: Packets of jelly, (angel delight?!), custard powder or tetra packs of ready made custard, pack of pudding rice, tins of fruit. Do you keep a can of squirty cream? Do you like special marmalade Christmas morning, do the DCs get nutella as a seasonal treat or does MIL like a certain jam on her toast? Also porridge oats (for brekkie or baking) or other cereals.
Hot drinks - tea (regular and any special ones like chamomile, green, fruit ones etc), coffee (ground, instant, decaf, pods for a machine, and filters if you have that kind of machine), hot chocolate or cocoa, Bovril, etc.
I don't tend to buy boxes of sweets or tins of biscuits - I buy a selection of nice packets of biscuits so I can put out a selection on a plate but only open as many packs as we'll likely get through (to avoid them either going soft or me eating all the leftovers). I do the same with crackers for cheese - a few nice different packs rather than the box of mixed ones (with only 3-4 of each type!) as we eat cheese a lot over the holidays. I also tend to get things like a couple of packs of microwave popcorn for afternoon movies or snacks, sharing packs or multipacks of crisps, nuts etc. I also get a packet of amaretti biscuits as my treat to me.
You can stock up on drinks too - large bottles of fizzy drinks or squashes, mixers etc. And alcohol - spirits, nice wines, a bottle of fizz for a special occasion, box of beer etc. I would tend to get these when they are on special offer though.
Don't forget to stock up on cleaning things, especially when they are on special offer. Especially ones that are easy - so I tend to have a couple of packs of wipes for counters, floor etc that I wouldn't necessarily use the rest of the year. But also get stocked up on your regular items. Dishwasher powder, salt and rinse aid (and you may as well get a dishwasher cleaner too for the week before to make it sparkle!). Washup liquid, soap, bleach, bin bags. Toilet rolls and kitchen towels. Greaseproof paper, tin foil, cling film, bun cases. I sometimes buy a pack of tin foil pie plates and portion packs - so that I can make an apple tart to freeze when I have spare time over the autumn, or an extra portion of a family meal to bring out when time is short or be able to freeze a meal-sized amount of leftover turkey. Serviettes, paper or plastic plates and glasses if you use them for parties.
These are all long term storage items - from early December you can start to get things with shorter shelf lives, like long life croissants and pain au chocolats, part baked breads, tins of ready rol croissants for the fridge, pizza bases, bag of grated cheese, pack of sliced cured meats (pepperoni, parma ham, salami, etc). And of course, if you have freezer space, things like veg, ice cream, emergency pizza/wedges/oven chips/chicken goujons/fish fingers etc., and your own stores like rolls of cookie dough (although you can now buy that too), HM mince pies, stuffing you've made ahead of time, or even just the breadcrumbs you make a week you have a couple of leftover slices of bread.
Sorry this is so long - it's meant to trigger ideas.
I tend to think of a stocking as containing a clementine, sugar mouse etc. but I am old