Mattresses (including for the pram carrycot if you get one), car seats and bottles and dummies if you are going to use are the only things you need that need to be brand new.
Absolutely necessities are:
Some way to transport baby - so baby carrier and /or pram. Both are definitely worth trying before you. Find a local sling library to try out carriers and for the pram I’d recommend having a nosy at a big pram centre type store and then buying second hand. Imo it’s worth buying a really good pram, especially if you’re buying second hand, but a really good pram is the one that going to fit your family and lifestyle best so have a think about how you’re going to be using it most - popping it in out the boot if the car all the time or lots of time on public transport ? Big long walk over different terrain or zipping about the city centre?
Somewhere for baby to sleep - if you can fit a cot in your room, I’d recommend just putting them down in the cot from day 1. Less to buy and one less transition for them that could potentially disrupt their sleep.
For naps I just put them down in the carrycot from their pram or on a blanket on the floor (and soak up all the cuddled in contact naps you can ☺️)
You’ll also needs sheets, a mattress protector and a sleeping bag plus a spare of each for when the have a blowout/ their nappy leaks/ they spit up all over them in the middle of the night 🥲
Something for them to wear: Buy a bunch of sleepsuits and vests and maybe a couple of cute outfits for showing them off and taking pics. After having had a sicky baby who could get through a dozen outfits a day I always recommend buying more clothes than you think you’ll need, they cost next to nothing second hand and take up very little room at that age. Have loads of newborn and 0-3 and maybe a pack of tiny baby. A few little cardigans a couple of hats and a maybe a pramsuit depending on the time of year.
not clothes but a couple of cellular blankets and a fleece or knitted one is useful too
Feeding - Loads of muslins. Some bibs (a find the hanky/triangle type dribble bibs best pre solids). About 8 bottles, a bottle brush, some way to sterilise them if they’re the pop in the microwave kind and one or two tubs of formula if you’re planning to bottle feed.oh and the next size up teats are helpful to have in before you need them. Not technically a necessity but a perfect prep or rapid cool or something similar is a sanity saver if you do end up bottle feeding.
You don’t strictly need anything for weaning but a basic highchair ( I prefer the basic folding ones to the ikea one) and an allover type bib is helpful. And little tubs to freeze baby size portions of things are useful too.
Nappies - buy a couple of packs of size 1 and a box of wipes but don’t stock up if you’re using disposables. If you’re using cloth I believe there are nappy libraries similar to the sling libraries. A little fold out travel changing mat is really helpful too.
Bathing - a really basic baby bath and something to support them in it. Plus some way to trim their nails and maybe a little brush in case they arrive with a full head of hair You’ll probably get gifted all sorts of lotions and potions and they don’t need them right away anyway so I wouldn’t buy anything like that except maybe a tube of nappy cream.
For you: Maternity pads/ or pants, breast pads and a peri bottle. I always recommend an insulated cup like a stanley or a good travel mug you can drink out of with one hand while lying in a weird position and stocking up on a bunch of your favourite easy snacks before baby arrives 😁
Other bits : a bouncer seat is good but don’t spend a lot - some babies love them, some hate them.
A couple of toys and books but you’ll provably get these as gifts too.
And after all that I’ll say as long as bay is fed, clothed and has somewhere safe to sleep, you can figure the rest out as you go.