We also waited till after our 20 week scan to buy anything, with the exception of a set of star wars sleepsuits!
That was a personal preference though - you can really look to start buying stuff whenever you feel comfortable doing so. There can be lots to buy so it might be helpful to start sooner to help spread the costs.
However, as noted above, key things you 'need' immediately are somewhere for baby to sleep, something for them to wear, and a means of getting them home, plus bottles / steriliser / formula if you're not planning to breastfeed. Things like a pram / travel system will depend on your particular situation.
I'm 26w now and feel like we've got all the 'big' stuff - big stuff for us included:
new car as our old one wasn't big enough! :(
car seats
pram
nursery furniture set [cotbed /wardrobe / drawers]
bouncy chairs
breast pump
We've also started on some of the smaller stuff inc:
Nappies & Wipes (disposable & reusable)
Muslins
Feeding pillows
Breast pump
I've separated my 'to buy' list into three sections: baby; mum; household. So on the baby list I still have:
Scratch mitts
[More] muslins
Bottles & steriliser [I'm hoping to breastfeed but also express so DH can feed]
Changing mat/s
Bath & towels
Blankets / bedding
Mobile for the cot
Room thermometer
Baby toiletries [e.g nappy cream, baby wash/soapy stuff]
Bibs
Nail clippers / thermometer / baby first aid kit
Baby monitor
Couple sets of sleepsuits [we're not planning on buying many clothes as we've both had friends recently have babies and we'll get plenty given, which we're very grateful for - every little helps etc. Though the stupid pandemic is making the logistics a bit difficult.]
Mum list is stuff for my hospital bag, e.g.:
Nursing jammies & bras
Maternity pads
Nipple cream
Breast pads
Slippers
Toiletries
Simple snacks / drinks
Household list is where things like the furniture and stuff for the nursery went, plus plans for pre-arrival meal prepping.
Hopefully that was helpful! A lot of things will depend on you and your personal needs / wants - I am sure we've got plenty of stuff on our list we could manage without. But these are the things we're planning on getting. So we're just slowly working our way through the lists, some stuff will be fine after babies arrive [e.g. we don't plan to get a baby monitor until they move into their own room] but it helps me to keep a track that we can tick off as we go as I was getting totally overwhelmed trying to keep everything in my head.