Ours is 9 months old, and I read and planned a lot, didn’t get a bunch of the stuff they think you need (mostly happily), and this is my list:
Someplace for it to sleep (crib, in bed with you, crib for later and Pack and Play in your bedroom for now, crib for later and bassinet for now, etc.) We bought a crib, the cheapest one you can get pretty much - the cheap IKEA one - remember that cribs, like a few other things, are regulated and all equally safe. It is not recommended to get a used one because these things get recalled all the time and there are styles which are no longer considered safe. Seriously. $70 bucks at IKEA. Mattress. Sheets for it. Done. We did keep him in our room for a few months in the bassinet attachment of a pack and play. He actually slept better in the crib though. Remember that just because they sell you something doesn’t mean it’s safe - many crib bedding sets come with bumpers which are not recommended or a quilt which you should never put in the crib, so it’s… just for decoration?
Some way for it to ride in a car. Some people use an infant-capable convertible seat from the beginning and wear the baby when out. I considered that but went with the infant seat you can take out anyway, and was glad I did until he got really heavy. It isn’t just a way to carry the baby, it’s also, for example, his own semi-private germ-free space in a restaurant. This is the other thing you must buy new unless, like, your sister has a seat to give you that you know has never been in any kind of wreck and has not expired.
Your car seat may inform your stroller selection. Newborns can’t do the umbrella stroller thing. The best stroller for you depends on your lifestyle. The people at lucieslist.com do a really good job breaking down the pros and cons of all the models and styles (and on everything else your baby needs, too.)
Something to keep it from shitting on you. We use cloth diapers. Not for everybody, not as hard as you’d think. If you get cloth, get real quality cloth or you won’t be using it for long. Disposable is of course the other option; don’t go crazy and overbuy newborn size because some babies never wear them (and some babies stay in them for awhile). They will take unopened boxes back in exchange for the next size up. You also need some sort of wipe arrangement. You need some place to put the diapers when they’ve been used - some people swear by the diaper genie, some people hate the expensive refills. One way or the other you’re going to have a bucket of human feces in your house, so plan a workflow about that. (We have a kitchen trash can with the flippy lid and a washable liner in it and we do diaper laundry a few days a week. Dog has never bothered it, thankfully.)
Something to carry all the things it needs around with it. You can use your old backpack if you like. We do have a dedicated diaper bag (it’s a Skip Hop that I got an incredibly good deal on). Don’t overpack this thing unless you are climbing Everest with the baby.
I HIGHLY recommend also packing a Super Emergency Last Resort bag in your trunk. Put that formula sample you got in it, a bottle, a few diapers (even a real cloth diaper or two, not that Gerber crap, this is for real emergencies), a change of clothes for the baby and for you, anything you can imagine being desperate for. This is for if you forget your diaper bag, or your car breaks down, or if your baby shits out of all the clothes you brought. We’ve only needed ours once but if we hadn’t had it we wouldn’t have had anything to feed him an hour from home.
Some way to bathe it. In a pinch you could always put a towel in a sink, but obviously a tub is way easier. We registered for a nicer little sink tub but the baby came early so my mom ran out and got us one of these little guys. All you need. Fit perfectly in our kitchen sink until he got too big for that and then worked fine in the bathtub. Recently he outgrew that so we put him in a laundry basket. You also need some baby shampoo, something to moisturize it with (coconut oil, baby lotion, whatev) and I do think baby towels and washcloths are worth it although not everyone uses them.
You want to be prepared for when it gets sick. Diaper rash cream (if you use cloth you have to get cloth-safe creams, FYI), infant Tylenol and ibuprofin, a snot sucker (the Nosefrida is well reviewed - ours has never really been very snotty so it hasn’t so much come up), rectal thermometer. Aquaphor is great for weird bizarre newborn skin things. And you need nail clippers unless you’re my mother who thinks everybody should bite off their baby’s nails. Weird, Mom.
It has to wear some sort of clothes. Let people buy them for you and go to Goodwill. Seriously. New baby clothes are for suckers. Get a variety of sizes.
It’s going to ooze fluids. You need a lot of receiving blankets, especially if you get a spitter.
Most babies sleep better swaddled. You can do this in a blanket, especially one of those nice Aden & Anais ones (which are also great sunshades) but we liked the velcro swaddler things.
You need some way to feed it. If you plan to do this with your boobs, you will probably need some nipple cream, nursing bras, etc. I liked the Boppy and the Brest Friend, a lot of people don’t. Common shower gift though. You’ll probably need a breast pump also unless you plan on never being away from the baby or never having anybody else feed it, ever. (Also bottles.) If you plan to do this with Science, you’ll need bottles again, formula (unless your baby has special needs get the cheapest formula you can get as long as it doesn’t come from a Chinese melamine plant, that stuff is regulated), a bottle brush. We got a cheap little formula mixing pitcher that we love love love, it really does make life easier. You do not need expensive bottles. You can get them if you like them, but we use the Evenflo glass ones and they’re like 3 for $9. (We got the glass not because of BPA but because plastic just doesn’t seem clean in the dishwasher to me.) You do not need to sterilize them. You wouldn’t sterilize your boobs, would you? No. You would not.
A baby carrier is helpful. Try the Infantino Mei Tai once it’s a little bigger, it’s really cheap and you can decide whether you like the different kinds of carriers. The Moby Wrap is good for newborns. Don’t get one of those Bjorn-ish things where their legs dangle because a babywearer will berate you in public.
It is also EXTREMELY helpful to have a place to put the baby down in every room you spend a lot of time in. We were given a Rock and Play, which is a nice thing to have, but we ended up dragging it back and forth. Then we got a cheap little bouncer to put in the other room which was a godsend. It was also the only thing that would make him stop crying when he was really gassy as a newborn.
That’s pretty much all I can think of that I’d consider the “basic kit”. You do not need a wipe warmer. (Imagine what happens when your baby gets used to warm wipes and you have to change him somewhere else!) You do not need a swing, although many babies sleep well in them. You definitely do not need a goddamned Moses basket that matches your nursery, although of course if you want to buy one there is certainly nothing wrong with it if it makes you happy. Note that this list is tuned to people living the basic American car-based lifestyle and people buying things regulated by the US government; some things might be different in other places.
ETA - when you register at stores they give you gift bags. This is a great way to score, say, a can of formula even if you aren’t planning on using it, and you’ll have it for emergencies. We also said we weren’t using pacifiers, but were eventually very glad that we had four or five brands to pick from in our “drawer of crap they gave us”.
but the hospital will send you home with enough to be getting on with. Likewise, any old place to sleep will do at first. My daughter spent her first few nights in a large cardboard box that a pair of knee-high boots had come in (lined with blankets).